A fighter isn't doing more with their action, what are you talking about? A +3 weapon doesn't give more attacks or more abilities on those attacks, it just increases the numbers.
And sure, a wizard with a staff of fire is not, on a turn by turn analysis, doing better. But on an adventuring day analysis, they are essentially getting, what? Three more spells per day? That is very good, because remember, the entire supposed conceit is that the wizard's spells are better than the fighter's actions, but the wizard has a limited number of spells. Giving them three more spells per day means they are getting three more actions better than anything the fighter could possibly do, meaning the fighter (with their limited hp) would need to fight more battles to catch up. It also, by giving spells you don't need to prepare, assists in the whole "always prepared" trope. A wizard who doesn't need to prepare fireball because it is in their staff now has a free slot to prepare something else to solve a situation fireball couldn't have.
Interesting. So, you realize the wizard is going to 22, right? Just because you have a +2 cloak doesn't mean you don't have shield. You seriously underestimate how easily a wizard can get high AC. Heck, the bladesinger? They can have 19 AC and jump to 24 when they are actually attacked.
And even if it is just a subset of wizards, they are still a group of wizards who can do the fighter's job, and you are completely ignoring the clerics, the druids, and the bards as well.
And by level 8 the wizard can have three feats. Do you really think that a single feat is enough to off-set all the advantages of spellcasting we've laid out?
Oh, and "how the game is played in reality"? According to WoTC their data (which should be pretty good and accurate data) is that 50% of games are featless. So... in reality, a significant number of people are playing as the game was designed.
And, again, you seem to be ignoring things. If you have sharpshooter, how does Sentinel increase your combat ability? Or Polearm master? Or Shield Master? They don't. Again, once a fighter picks a path... that's generally it. There are only an incredibly small number of combat feats that synergize.
Right, you are looking round per round, but power isn't only generated round per round. A wizard who can cast three more spells, and have a 30% increase in their spells known is more capable of solving more problems, longer. And you don't seem to understand that spellcaster feats tend to stack. A spellcaster with Warcaster, Spell Sniper, Elemental Adept, and Fey-Touched can benefit from all four of those in a single combat without losing any effiency. A fighter with Sharp-shooter, Great Weapon Master, Shield Master and Tavern Brawler... can't. Those are all exclusive abilities that don't stack.