I think the OP was about safety, not speed. Presumably speed is not a concern. However "safety" is going to vary with the rider and their objectives. Firstly, the tire width should be appropriate to the rim width. That's for sure a safety thing. See
Sheldon Brown's sizing chart. Beyond that, if one is riding paved roads, a relatively narrow tire will be safer cornering, say no more than a 28 on a "normal" 13mm or 15mm internal measure 700c road rim. We've toured our 350 lb. all-up tandem on 28mm tires over cobbles and really horrible European gravel farm roads in complete safety.
However, if you're going to ride a lot of gravel, especially loose gravel, the wider the rim and tire, the better. I don't suppose there's really an upper limit there. However that sort of punishment will mean a heavier tire, too. Light wide road tires aren't going to be reliable. You'll get sidewall cuts.
IME there's no difference between narrower and wider tires w/r to pinch flats. That's simply a matter of knowing the correct tire pressure for your weight and maintaining that pressure.
As others have said, safety is much more a matter of bike handling than tire width.