Well, sniper rifles are a specific case (I have a sniper as my main); they are designed to excel in locations where you have command over the battlefield and forewarning of whats going on. In a situation like these, trying to force a sniper rifle in there is going to almost always be a losing strategy.
That said, I don't think I've ever been in a situation yet where I can shoot targets at a rate "barely sufficient for one mission," and i'm a fat middle-aged man with no real twitch skills or shooter experience.

As long as you keep moving, I've found, and pull back when tactically needed (and not use the sniper rifle in the middle of a pitched combat), I've not had too many problems, generally speaking.
And honestly, overlapping emergencies -- well, as long as they are of a different 'enemy type at least -- I've found to be much easier actually. Even if you do cheese off one of the groups, or the other, some judicious retreating, dodging and rolling tends to make sure that eventually one of them will shoot the other, and before long, they're fighting each other, allowing you to head back in and start shooting the guys already being targeted by the opposing forces.
See, I've seen this mentioned by other players, but I'm honestly of the opinion something else is going on and it's not necessarily the game/AI. I regularly stand behind cover, shooting over low walls, etc., and I can't think of any period where the bullets seem to 'magically' go through buildings, or hit me with perfect aim. I've seen enemy fire ricochet off my cover harmlessly regularly, and I've rolled out of the way of sniper fire, etc. Heck, I've often found a good defensible spot and just rip through an oncoming group while most of their shots bounce harmlessly off of cover.
I'm wondering if there's other causes in play here with some of these folks that seem to be 'magically' shot all the time.