The laser pistol is not a niche weapon. It's very effective against mechanical and cyborg targets and has essentially infinite free ammo available.
So, that's part of what I left out when I rewrote the post. I'll go over it now.
The Laser Pistol is niche, because the regular Pistol exists. I just wrapped up an Impossible run where I killed SHODAN with Standard 4, Modify 2 Pistol (unmodded) in about 2-3 seconds (not counting the time spent throwing ICE Picks at her). It's arguably the best weapon in the game, if you factor in it's availability. All but OSA Agents get access to it for free. Ammo for it is plentiful. And there are so many pistols just lying around the game that you can easily just keep swapping out broken ones for working ones until you get to 3-4 Maintenance, in order to never have to buy Maintenance tools. What's more, it has access to Armor Piercing Rounds. These specialize in killing exactly the same targets as the Laser Pistol. While AP Rounds are limited in supply, the Pistol can fire in bursts, while the Laser Pistol is stuck on a long recharge cycle. The Pistol can tear through enemies MUCH faster. And early on in the game, you have a fairly generous supply of AP Ammo as long as you're conservative and save it for needed targets (Droids can take standard ammo, and midwives can take the wrench). If you get the Grenade Launcher (Marine Start or Repair 2), that's another weapon you've got for turrets and bots. While you don't get any early EMP Grenades (I think) the GL does enough damage that it fulfills the same niche of doing lots of damage to your toughest enemies.
So the Laser Pistol competes with the other two Tier 1 weapons you get against the hardest early game enemies, only really winning out in terms of 'free' ammo. However, the ammo isn't really free. Going through the Cargo Bays, a Bot took 80 energy out of my Laser Pistol. Turrets took 40. That's a bot and a turret, or three turrets for between 2 and 5 Maintenance. The ammo may be replaceable, but you're not running back and forth from the recharger that often. So if you want more frequent use, you need batteries or Electron Cascade. And at that point in the game, you probably aren't swimming in batteries, and Electron Cascade is out of reach for someone with poitns in Energy Weapons and Repair. Simply put, you still need to use melee, other weapons, or some rare 'ammo' to keep going. The Laser Pistol also has the worst DPS, and in an extended fight is much more reliant on cover than a Pistol with burst mode AP round, or a Grenade Launcher. Both of which are also pretty darn good at handling biological targets (though you're not realistically using grenades against hybrids and monkeys).
Now don't get me wrong. I really like the Laser Pistol. But it has some pretty serious competition in the 'killing early to mid-game robots' category. And so that's why I call it a niche weapon. It directly competes with the other Tier 1 weapons, and it's strongest claim to fame is it's ammo system. That's a niche. It's a good niche. It's a niche I like, but it's still a niche. Throw in the fact that Heavy and Standard Weapons will happily get you through the whole game on their own, while Energy Weapons has an entire level where it's utterly useless, and that doesn't help the case against being a niche weapon.
And so it just doesn't make sense that you get the Laser Pistol so late without the Marine Start, while the GL is available halfway through Med/Sci with Repair. For reference, once I got the Laser Pistol from Engineering working, I fought 3 turrets and 2 midwives before I got the working one. I could have skipped one turret and one midwife from the Engineering 'tunnel'. I could have skipped the two turrets guarding the recharger and OS station by running by them if I had to, and coming back later with the Laser Pistol. It's honestly not really worth getting Repair just for the Laser Pistol (though it IS worth getting repair for the EMP Rifle, given it's ridiculous Maintenance requirement, but oddly low Repair requirement), because there's so little you really get from it before you find the working one. If you want a lore appropriate place to stick a broken one, put it outside the armory (or behind the forcefield) in Med/Sci. And I'd leave a working one in the Cargo Bay areas outside the actual Cargo Bay, so you have it against the small army of droids, bots, and turrets.
But not against the three turrets guarding the entrance to the Cargo Bay, which are a nightmare for an OSA character that didn't dip into Pistols, or really anyone who ran out of AP ammo by then. I think that's a nice extra place to reward Repair users, in addition to it's various uses in Med/Sci.