Lets look at this rationally
and with a bit of historical perspective, shall we?
Early handguns all had fixed sights, if they had any kind of sights at all. Colt cap&ball pistols (revolving pistols) had a small V notch cut in the hammer, and a tiny front sight to align through it.
By the 1870s, you have solid frames with a channel to look through to find the front sight. The best of these had a square notch at the back. Along comes adjustable sights. Add ons to regular fixed sight guns, for target work. Generally pretty big, clumsy and fragile. Easily knocked out of adjustment, easily damaged. They get a (deserved) reputation as not suitable for serious social use.
Time passes. Adjustable sights get better. Smaller, more durable, but, the reputation persists. Adjustable sights are too "fragile" for police work.
GI guns stay fixed sight revolvers, and the 1911A1, which has the rear sight drift adjustable for windage. Works just fine for them, as the military only shoots one load, and they don't put as high a premium on accuracy as civilian owners do. Most service autopistols still follow the same basic sight pattern, a fixed front, and a rear sight drift able to correct for severe windage problems.
Now move into the 1930s. Things start to change. The .357 Magnum becomes the tip of the iceberg, showing shooters things that powerful handguns can do, and that they will do them better with adjustable sights.
Pause for WWII.
Move to the 1950s, and enter the .44 magnum. Again, much more useful tools with adjustable sights. By this time, the adjustable sight has proven itself capable of surviving police use, and some agencies do use them, notably Hiway Patrols, but many do not. Still considered "too fragile" or an "unneeded expense". But civilian shooters want them. Because of their versatility. Many gun models are marketed identical, excpet for the sights. And Every gun makers top of the line models feature adjustable sights.
The drawback to fixed sights is that they can only be "on" for one load, at one range. Lots of loads will be "close enough" for many things (especially close range defense) but for other things, shooting at longer ranges, hunting, etc. you are best with a gun that shoots where the sights look.
And fixed sights can't be easily changed, and can't be repeatedly changed. Every gun is an individual, with individual quirks, and slight to not so slight differences of how they shoot different ammo. No two people seem to look through the sights exactly the same way.
With a fixed sighted gun, you have to find ammo that shoots where you look, and stick with it in order to be on target. Or you need to learn the hold off for each different load, and range you are going to shoot.
With an adjustable sighted gun, you can adjust the gun to both the ammo, and you, and when something changes, you can adjust it again, over and over.
Do you need adjustable sights on a belly gun? no. Need them on a ccw? no. You don't need them on anything, if you are willing to put up with what you have to do to make fixed sights work their best for all the things you do with a pistol. I had a fixed sight .44 mag.(Ruger Vaquero) nice gun, but I traded it for a SuperBlackhawk, because I wanted adjustable sights. Because I do different things with my pistols, at different times, and I like to be able to zero the pistol to the ammo I want to use, not zero myself to the ammo the gun likes to use.
Lots of shooters don't adjust their sights often. But many, if not most, have adjusted them at least once. Once the get the gun/ammo combination shooting the way they want, they often leave the sights alone, until something forces them to adjust them. And when it does, they are glad they can. I do own a fixed sight revolver, but its outnumbered about a dozen to one by its adjustable sighted cousins.
Compared to service style semi autos (1911s or any Browning style tilt barrel system) revolver sights are often more accurate. Individual guns can be exceptions, of course. But generally its true. Because revolvers have the front sight on the barrel. And the rear sight (fixed or adj.) on the frame, and in relationship to the barrel, these sights do not move.
Autopistols have the sights on the slide. And the barrel moves, the slide moves, and hopefully everything comes back to the same place for the next shot. Take a look at most of the "sport pistols", the .22s. Rugers, Brownings, Colt Woodsmans etc. They will almost always out shoot a service pistol, in terms of accuracy (group size). Why? Because their barrels don't move, and at least one of the sights is fastened to that barrel!