Fighters definitely don't suck in 5e. I've run and played several fighters and haven't found them to be weak. One of the key things to remember about 5e fighters is that they are a short rest based class. So if a DM isn't letting the party take short rests they'll lag behind, but a well rested fighter can bring a lot of pain. And the problem with bounded accuracy effects all classes, not just fighters and fighter's have the easiest path to a high AC. It also applies to enemies, so a high level fighter is going to hit often and hard, so while you may be taking damage, the enemies will be as well.
I also haven't found burning hands to be to overpowered. First, it requires the caster to be fairly close to the enemies and second, Dex is one of the more common saves in the game, so full damage is not a guarantee. Usually, a cantrip like Firebolt is the more cost effective and reliable option.
As for enemies, I just adjust on the fly if they're carving through PC's to fast or lasting to long. CR is a tricky business at the best of times. But, the bring up my earlier point, bounded accuracy makes hitting a lot easier. So that ogre might have 59 hp but it only has an AC of 11. A level 3 fighter with decent stats (we'll say strength of 16) has a +5 to hit and will hit more then half the time.