Kinda going back to something said at the start of the topic but I've actually thought a lot about why the pistol and the chaingun both use the same ammo, outside of simple gameplay abstraction, and there is a pretty good way to rationalize it.
See, the player and his compatriots are space marines, right? Meaning that they primarily operate in spaceships, space stations, bases on planets without breathable atmospheres, so on and so forth. These are places where shooting through walls would be a very, very, very bad idea because hull breaches aren't fun. Aside from that, you could maybe hit important stuff that keeps the whole facility running/everyone inside the facility breathing. Hideous Destructor addresses this by stating that the 4.26mm caseless ammo fired by the mod's standard issue rifle are frangible, i.e. they're designed to fragment when hitting harder stuff like walls.
Another way one could conceivably space marine-proof a weapon system is to simply use ammunition that just isn't as prone to tearing through walls. As it happens, pistol rounds and buckshot are pretty good types of ammo to turn to if that's what you're looking to do, hence why submachine guns were in use by police forces long after they went out of style for military applications; they're more often fighting in areas with innocents potentially behind walls. So, yeah, that's why everyone seems to be armed with pistol-caliber carbines, shotguns, and weird lightweight low RoF rotary guns...
Which on that note, that too makes sense when you consider that guns overheat ridiculously fast in a vacuum with no air around them to air-cool them. Multiple barrels, whether rotating clusters of them or quick-swapping ones, have long been the terrestrial response to overheating issues in guns; I see no reason why they wouldn't carry on this tradition in space. Advances in metallurgy allow them to make such a weapon that's light enough to not just be man-portable but even wielded in one hand(see: chaingunners), and it's a good answer to the problem of needing reliable automatic firepower that functions in a vacuum.
TL;DR - The pistol and chaingun share ammo for safety purposes because space marines are in space and poking holes in walls is bad.
As for the actual question posed in the topic, I've always felt the pistol exists to hold you over until you find something nicer, and that's perfectly fine by me. It's a thankless job but it's one that has to be done, and I for one salute the pistol for doing it.