TL;DR: Typically soldiers don't know the direction of enemy fire unless they've specifically seen the enemy firing at them. The most they do is make the snap-decision and hold to it as per their training when responding to direct and indirect contact within any battlefield.
See the events surrounding the attack on SPC Tschiderer here: Gun Camera footage from his would-be assassin.
This is a relatively close-range engagement on a crowded street in Baghdad, admittedly made from great concealment. The sniper had every ability to take down the soldier, but waited for a viable Center of Mass shot. It just so happens, that the Department of Defense has done its research and determined that the CoM is the most vital area to cover and thus have made body armor specifically protecting that from multiple direct blows.
It is more often than not in the battlefield that indeed you get shot from the direction you're not paying attention to. I believe the statistic for most combat pilots shot down in world war 2 was something like 80% that never even saw the enemy that engaged them? The fog of war is huge in a combat zone, it's something we get taught a lot and it's why it's vital that you train everyone to the same standard of being able to hold a defensive line because if your line is broken at any point, it will become a fact that the rest of the line will fall unless you happen to have extremely well-prepared backup or reserves that can quickly move in to plug the line before the breach is exploited.
The idea of wearing anything on my back is also incredibly unappetizing. If I was told that in addition to the camelback for my water, the assault pack for my additional equipment and ammunition, and perhaps even my entrenching tool if I feel a bit Ukrainian that day, I also needed to lug around an additional bullet-proof armor plate, I doubt this would do much to bolster my confidence in my already fairly adequate equipment. If anything I'd feel the need to generally disregard using it unless I managed to take a hit to a main plate and for some reason was still present on the battlefield with the need to replace the armor plate.