If the wizard is flying, they should be able to walk on the wind because they're awesome. They should be able to smash mountains, run really fast, dance on the tips of spears, lasso tornados, and straight up not die. If Pecos Bill, Cucuhlainn, Roland, or Benkei could do it, so can the fighter. I suspect I will get many comments about the terrible anime fighter and how real fighters are totally mundane warriors who are somehow worthy of respect by guys who can fly around, teleport, turn invisible, and conjure armies of minions, but quite frankly the "mundane only" fighter is a joke which falls apart the first time your fighter deals enough damage to wreck a main battle tank or survives being sat on by a dragon.
The people who want a game to do things in the highlighted section are better off not playing D&D. D&D has never had these things possible, and I'm not interested in playing a game where they are possible. If I wanted to play that kind of game, I would play Exalted.