I've done campaigns to 20th level - in multiple editions.A few random thoughts on this. First, I have no problems with people playing fighters and wizards up to 20th level. Yes, the wizard can go nova, but the fighter is the energizer bunny that just keeps going and going hacking and slashing. I played a way of mercy monk in one of my previous campaigns and now another player wants to play a monk and my wife is planning on playing one in the campaign I run because they were so effective.
First - yes, technically the fighter can "go all day..." while the caster is reliant on limited spell slots. But, in practice, the fighter tends to run low/out of HP as or more quickly as the casters run out of spells - especially as levels increase.
Second - In my experience, in a "typical" campaign, fighters need A LOT more attention given to special items (swords, armor, belts etc.) to stay even close to par with the casters - who certainly LIKE cool items, but they have spells and don't really need them.
Third - D&D, as a default, is a game that relies on attrition. If the DM doesn't pay attention to that and doesn't have enough to drain caster resources (in whatever manner) they will dominate. I'm in 2 campaigns right now where 1 DM is paying some attention and the other is paying 0 attention to this. The one where the DM is paying 0 attention is a REALLY fun campaign the DM is great, BUT the casters are utterly dominating in nearly every situation because 90% of the time they have their full resources to devote to any given encounter.