Subjective brightness of a short flash can be higher (briefly) than for a longer flash because the visual system lags in processing time relative to the flash duration [38]. Rinalducci and Higgins [39] conclude that increasing the duration of the flash for signal lights longer than 0.2 s will not appreciably improve its conspicuity.

When flashing lights are employed (e.g., to increase conspicuity), sources with rapid onset times provide modest reaction time benefits.

A number of studies have suggested that flashing lights increase the conspicuity of a signal relative to a steady-burning signal light, but flashing lights, by virtue of their reduced total light energy, can have disadvantages relative to steady-burning signals as well.

Well above visual threshold, the detection of a signal light that is steady burning is improved over a flashing signal light (with a maximum intensity equal to that of the steady-burning signal), in a manner consistent with effective intensity [27].

From a safety perspective, a couple of studies have looked into the effectiveness of blinking lights compared to continuous lights

A Dutch study reviewed various types of bike lights and found that drivers notice blinking lights sooner, but have a harder time judging the speed and distance of a blinking light than a continuous light.

Wood et al. (2009): Drivers’ and cyclists’ experiences of sharing the road: incidents, attitudes and perceptions of visibility. Accident Analysis and Prevention, 41 (4), pp. 772-776

About differences in the visibility as perceived by bikers and drivers:
The largest difference relates to the visibility of cyclists using lights on their bicycles, where cyclists rate themselves as significantly more visible when using bicycle lights than did the drivers. This difference, in turn, is much greater at night than during the day.
Visibilty on scale 1 to 5; parentheses: standard deviation.

So cyclists think they are both equivalent, with a possible small advantage for the steady light, while drivers thought the flashing lights to be more visible (but remember differences between detection and recognition, see below) to be better, but still less visible than the bikers thought the flashing light.

With regard to the distance:
An analysis was also performed with regard to the average distance at which drivers and cyclists believed that a cyclist would be visible to a driver using low-beam headlamps at night. On average, cyclists believed themselves to be visible from 110.3 metres (sd = 157.662), while drivers believed a cyclist would only be visible at 48.3 metres (sd = 58.69) on average (that is, at less than half the distance estimated by the cyclists), t (1424) = - 9.247, p < .001.
Probably even more important than deciding whether flash or steady light is better, is actually using the light:
While the use of visibility aids was advocated by cyclists, this was not reflected in self-reported wearing patterns
*(emphases mine)s
Maybe this Cochrane review: Interventions for increasing pedestrian and cyclist visibility for the prevention of death and injuries is useful for background info, and they have a few comparisons of steady light vs. reflector and blinking light vs. reflector:
Blomberg 1986: A flashing light held by a pedestrian yielded a greater detecti on and recognition distance when compared with reflectorised accessories (420m versus 207m and 96m versus 92m respectively).
Watts 1984b: A rear bicycle lamp yielded a greater detection distance when compared with reflectors (306m versus 184m).
Watts 1984c: A flashing beacon on a bicycle yielded a greater detection but not recognition distance when compared with reflectors (588m versus 444m and 59m versus 71m respectively)

Steady daytime running lights, similar to what are used on motor vehicles, may not be enough to make road cyclists any more visible than if they went without. Remember that that selective attention phenomenon conditions drivers to look for other four-wheeled motor vehicles, so the odds are already stacked against us. Motorcyclists have used daytime running lights for years, for example, and that user group is all too familiar with how steady DRLs offer only modest protection against the driver that “just didn’t see you.”

Motorcyclists have since moved more toward flashing front and rear DRLs, and cyclists have followed suit.

“Brightness at the source does not necessarily mean bright where it is intended to be seen from; lumens are not everything,” said Applegate. “The lensing, flash pattern, and range of the light are equally important. When designing effective daytime running lights, you need an interruptive flash pattern that draws the attention of drivers. You want not just to be visible, but to be recognized. There is a difference.”

The "closing rate detection" isn't an issue. The idea is to be conspicuous from a long way away. Long before "closing" becomes a concern.

Why do they use strobes in rescue situations? Why do they use strobes on airplanes?

You want drivers to have as long as possible to be able to be aware of you (and have some idea what you are) for as long as possible. It makes the window larger (hopefully) than the distraction window or gives more time for your presence to reach their consciousness. This is the point of the flashing light (not the other thing).

And you are ignoring the other quotes.

Well above visual threshold, the detection of a signal light that is steady burning is improved over a flashing signal light (with a maximum intensity equal to that of the steady-burning signal), in a manner consistent with effective intensity [27]. When the intensity of a signal light is reduced such that it approaches the visual threshold, the relationship between steady-burning and flashing signals is reversed in opposition to effective intensity [27].

Conspicuity of target lights: The influence of flash rate and brightnessThe stimulus characteristics of lights that might aid a pilot to see and avoid, by alerting him to a potential threat were studied. The relative conspicuity of foveally equated, point-source, steady and flashing lights of several brightnesses, seen against a star background was examined. From the subject's viewpoint, these target lights could appear anywhere within a large (40 deg horizontal by 35 deg vertical) field of view. The lights appeared at random time intervals while the subject was periodically distracted by a simulated cockpit task. The results indicate that correct target detection increases and reaction time decreases with increased target intensity. Steady lights are missed more frequently and acquired more slowly than flashing lights, but no significant differences are found among the wide range of flash rates employed. The intensity of the light has a greater effect on both detection and reaction time to steady lights than to flashing lights. These results are compared with results of other researchers who used targets which appeared at fixed locations. The longest reaction times were recorded to lights which appeared either at the extremes or at the very center of the visual field.

Mariners frequently have trouble distinguishing lighted aids to navigation in areas with a high density of background lights. The Coast Guard is seeking ways to enhance the conspicuity, or likelihood of being noticed, of these aids. Literature has shown that a flashing light is more conspicuous than one that is steady. To improve conspicuity by determining optimal flash characteristics, we had 20 observers search for a flashing point of light among backgrounds of steady lights on a CRT screen. In single 360-trial sessions, observers indicated which of five screen sectors contained the flashing target, and accuracy and response time were recorded. Targets were flashed at 1, 2, and 3.85 Hz, each at duty cycles of .3, .5, and .8. An ANOVA showed significant effects of frequency, duty cycle, and background light density. Search time increased with number of background lights. Conspicuity improved as frequency increased and as duty cycle decreased.

The findings indicate that there are conspicuity advantages of using lights with dynamic qualities (e.g., flashing or moving spatially), as opposed to static qualities when cycling at night.

This time, the researchers found, during the day, “that from a distance of 200 meters…a flashing tail light is significantly more conspicuous than an always-on tail light, which in turn is significantly more conspicuous than” no tail light at all.

The results indicate that active visibility treatments, such as bicycle-mounted lights, make cyclists more conspicuous than passive systems like retroreflective vests and biomotion bands. Flashing headlamps and tail lamps were the most conspicuous treatments during both the day and at night; fast flashing headlamps (6.7 Hz) had higher detection distances and rates during the day, and moderately fast flashing headlamps (3.4 Hz) had higher detection distances and rates at night. Spoke lights and flashing tail lamps, along with retroreflective vests, also aided cyclist visibility during the day and at night, especially for vehicles approaching intersecting cyclists.

The present study compares steady and flashing light signals with respect to conspicuity, defined as the speed of response to a signal above threshold. For large signal contrasts the conspicuity of steady and flashing signals is approximately equal. For small contrasts the conspicuity of flashing signals is considerably greater. These results suggest that flashing rather than steady signals be used for warning purposes.

Well above visual threshold, the detection of a signal light that is steady burning is improved over a flashing signal light (with a maximum intensity equal to that of the steady-burning signal), in a manner consistent with effective intensity [27]. When the intensity of a signal light is reduced such that it approaches the visual threshold, the relationship between steady-burning and flashing signals is reversed in opposition to effective intensity [27].

Even a small village is likely to have some lighting that will be maintained on throughout the nighttime period. Since the spatial configuration of such lights would be uncontrolled, the possibility of a chance arrangement similar to the corners of a runway cannot be eliminated. In such a case, both to improve conspicuity of signal lights and to differentiate them from other lights, the use of flashing patterns would appear to be beneficial.