I though we were talking about high level fighters.
It seemed to me that the comparison was overall, not just at high level. High level simply offers more dramatic demonstration because little can match the ridiculous power of many 7th+ spells.
I still don't understand why someone is playing a fighter if they want the breadth of versatility the wizard allows, or even what that would look like.
It is not, strictly speaking, a desire to have identical versatility. It is that the Wizard is SO incredibly versatile...while if anything becoming more and more capable of replacing the Fighter if they so choose...that is the issue.
Very early, you don't have enough spell slots to eclipse your Fighter colleagues. It's not hard for a Fighter to do better than what 2 spell slots can achieve. But once you get past that point, once you're in the middle tiers, Wizards specifically (and full casters generally) pull well ahead. Especially because the resting mechanics depend on incorrect assumptions about what players (and DMs) want to do. Partial casters likewise pull ahead of total non-casters. The Paladin is simply a stronger class chassis than the Fighter, especially the Champion, which lags well behind the Paladin in damage output unless specifically fed more and better magic items (mostly magic weapons with high bonus damage, but other bling certainly helps.) Or, to phrase that another way, Paladins can very, very easily put out equivalent damage to what the Fighter can do (being nominally "just as strong" at combat as the Fighter is) while still having spells left over for doing other things. Sure, it might not be tons of spells. But it's still a gap.
The thing we were sold on, back during the playtest, was that the Fighter would be (pretty much unequivocally) the best at...well, fighting. And that other classes would legitimately have to make sacrifices in order to get their extra benefits. In practice, that is simply not true. Fighters are about as good at combat as Paladins and Rangers, and multiple types of full spellcaster (e.g. War or Storm Clerics, Moon Druids, Bladesinger Wizards, Hexblade+Blade Pact Warlocks) can generally keep up with the Fighter in terms of fighting ability while having a HUGE pool of versatility on the side.
If Fighters are meant to be an equally valid option, they should either get special stuff that makes them stand out (be true specialists that cannot be matched by others), or they should be versatile enough to contribute to a variety of situations in the same ultimate manner as other classes, but in a different specific method or style. Otherwise, it is disingenuous or even outright deceptive to pretend that Fighters and Wizards are meant to be equally valid (NOT utterly identical, just equally
valid) options in cooperative play.