Can’t stress this enough. The F-91W is useless at night because the backlight brightness is terrible. The F105W has an indiglo-style “EL” light that is very effective. The two watches are nearly identical from an aesthetic perspective. The functions are identical as are the buttons.
But in either case, it's perfectly safe. There's no way to touch either the hot parts or the high-voltage parts. And even if there was, the battery doesn't have enough oomph to do anything more than tingle once the prickly part was trying to drive something as massive as a fingertip.
I noticed the noise too, when I owned one, but I figure silencing it would've cost size, weight, and power. And the noise was never more than a curiosity, so I'll take it!
However your comparison to incandescent and your point about the momentary nature are both valid I'd say. If they had magic, they'd have used it. So they took something fundamentally inefficient and added engineering to make the best of it. A bad thing, done as well as possible,
You could say almost the same things about incandescent. It's not electrically noisy, but temperature sure does perturb the timekeeping, and incandescent definitely wastes power. Especially if you need the filament to last indefinitely instead of replacing it easily.
'The small light bulb was replaced by a LED diode, but the intensity of the tired firefly remained'
https://www.hodinky-365.com/blog/casio-f-91w-review
I wear F-91W every day and FWIW, the light is adequate to see time at night.