The laser pistol is more of a SMG. it's pretty nifty for tight quarters inside UFOs thanks to its low LOW autofire costs.
And of course its the perfect sidearm through the entire game due to not needing ammo... but really why bother with a sidearm unless you are using a blaster/rocket launcher?
Most troops use heavy plasma and have nearly infinite ammo.
Mostly because I do use rockets up until near endgame. Then I use blasters a bit more. There's usually a couple of rocket/pistol soldiers though, even on the final mission. Heavy plasma is the standard assault rifle, but big kabooms never go out of style.
It's the rookie weapon of choice. Nothing gets that initial kill or two like a large rocket for such little cost. So I end up getting caught into the mindset that RLs/pistols=good. Even if it's not actually true when compared to other combos. But it's never actually bad. AoE never runs out of utility, and I'm too damn cheap to knock down buildings with blaster bombs or alien grenades, no matter how many of them I have. But a loaded launcher, a spare rocket, a pistol and a smoke grenade makes for the perfect soldier. Cheap, does stuff, not too heavy. Although I do tend to screen my troops for strength early on, rather than bravery (which is what I should be doing).
It's way quicker to waste one soldier's TUs knocking out an entire wall and giving everyone a sight lane than selectively autofiring through a wall with plasma. The amount of times this causes me to actually have to move half the squad because the wrong square or two got destroyed is annoying. Ssshhhmmm KaBOOM! Sight lane is open, begin firing. BTW, you're now you're a pistol man rookie. Have fun, you're going in first when we get to the UFO.
edit from posts below: Yep. This is why rockets still get used into late game. They might not be able to blow into UFO hulls, but they probably won't nuke half a squad in other situations either. With good armour you can even fire one at anything 5-6 squares away and not care (much) about the explosion. Which makes them awesome, and makes pistols awesome too.