Is there a reason given why you can't just take weapons from enemies that you've killed? For example, in the Metal Gear Solid series they (sometimes) state that enemy weapons are locked, through DNA or nanomachines or some such. Obviously, this is so the player can't just take an assault rifle from the first mook he sees and start blasting, but they've used the lore of the series to try and justify it. Is there a Codex entry that states something similar happens in the Mass Effect universe? I can't find anything on the Wiki that states why you'd have to wait until you find a weapon just laying around to be able to use it.
For instance, in ME2 you get the Vindicator from a couch in Archangel's base. At this point in the game you might have killed dozens of Blue Suns mercenaries who have been equipped with Vindicators. What's so special about the one on the couch?
Note that this may not be the case for the first game. It's been so long I can't remember if bodies were lootable or if it was just crates etc.