...This problem is not exclusive to UC3, it's actually much more problematic in UC2. In UC2, you legitimately get locked into a fight with a single soldier -- more commonly with the soldiers equipped with black-color camo (not the armored guys if they have their helmet on and not the weaker grey-camo guys ) and you would legitimately die if you got into a fight with a guy while others were around because you had to wait for prompts to show up or for certain animations to trigger during the melee.
UC3 doesn't have this problem with normal soldiers, the only time it can happen is with context sensitive melee animations. Things like Drake using their weapon to wack them with it, bashing guys over cover/walls, catching enemies' weapons after you've melee'd them and so on -- all of which typically are in slow-motion. Those context-specific animations are what's problematic in UC3 and even then they're not as bad as what UC2 did. UC2 was definitely worse in this regard ignoring the boring bald guy you had to melee in UC3 (which by the way in UC3 you can skip one of those fights, the one in the chateau to be more precise).
Point is, UC3's melee is way better than UC2's if you're smart about it. You can more freely mix melee and shooting in UC3 than you can in UC2. In UC2 you pretty much prayed you did enough damage for the drop kick and/or one hit punch (steel fisting as it is called in all three games, blindfire + melee) but if you didn't you'd trigger the same old "gotta wait until I can hit triangle to counter this guy" animation which took eons to occur in UC2.