Wheel with for a 28mm tire
 

I wonder how important is the external (or internal) tire width when fitting wider tires.

For example, would a wheel with an external width of 25 accommodate better a 28 mm tires versus a wheel with a 22 width?
Some Bontrager wheels are even wider (27mm).

I suspect there may be a negligible aero disadvantage when installing wide tires in slim wheels.

Or not?

It makes a big difference, as far as aerodynamics are concerned; wider wheel will result in a less bulbous/light bulb shape, which will help the aerodynamics. It will also help turn-in and general confidence.

I recently went from 15mm internal width rims to 17mm internal rim widths, both with 25mm tires (so even with the new wheels, still pretty light bulb shaped), and I still noticed an appreciable difference in turn-in response when leaning into a corner. Then again, I also swapped tires and tubes at the same time, and am on much lighter/stiffer wheels, so it's hard to quantify what parts are primarily responsible for various changes in feeling/performance.

That said, I don't really know what is truly considered the gold standard now for widths; it seemed like for a short while C17 was all the rage, but it seems we are already moving past that into even wider rims? Someone else can chime in on that. I imagine a C17 with a 28mm tire wouldn't be any better than an old C15 rim with a 25mm tire, so I suppose as 28s become more the norm, so too will C19s or whatever.

Also makes a big difference in the size and shape of the tire. The wider the internal part of the rim, the wider the tire and the higher the profile. That seemed counter intuitive to me until I looked at it and realized that the wider the rim, that rubber on the sidewall part of the circumference now goes into tire shape instead of tucking back into completing the circumference.

Matters if you're trying to get a bigger tire on a road racing frame that "accepts" up to 28mm. Maybe yes, maybe no.

These "advantages" people bring up for wide rims are not as great as they make out.
You will not be able to measure any aero advantage, especially if you are on a low profile rim.
You won't be cornering any faster either.
So if you already have the rims use them.
But if you want to buy new rims/wheels anyway, sure get something a bit wider.

I think to get aero advantage you need to be something like 1.05x the tire width.