I don't think the issue is antipathy toward fighters. I also don't think it's really about "realism". (I don't think that word should be used when talking about fantasy settings anyway; "verisimilitude" is a better word, but I don't think that's quite the issue either.)
One issue is differing playstyles: Some people may want their character to be Hercules, but maybe others want to play someone who doesn't have magic, like Hawkeye or Batman*. Someone proposed a tier list for level ranges, but I think people have different ideas about where to draw the lines and what the top end should be, and I think none of them are necessarily wrong. Perhaps this can be addressed to some extent by picking a different class or subclass.
The other issue is narrative justification. Why can a wizard create a fireball? Well, she's spent her life studying magic. Maybe you think at level 20, she's too powerful compared to the fighter, and that's fine, but she's breaking the rules of physics as we know it from level 1, with the lowliest cantrip.
But, HP wonkiness aside, the fighter at level 1 generally doesn't break any rules. Why, at level 20 can he suddenly cleave a mountain in half or divert a river? For a lot of people, the answer seems to be mostly "because it would be unfair if he can't do cool things like the wizard", and they are content to handwave it. And that's fine! But some people are not content with this explanation, and that's also fine! (And maybe being somewhat better than a normal person doesn't need an explanation, but to completely outclass normal people does. And different people may draw this line at different points.) Hercules, the answer is that he's a demigod; Superman is an alien who gets powers from our yellow sun; Peter Parker was bitten by a radioactive spider. The explanation doesn't have to be terribly "realistic", but for some people it needs to be there nevertheless.
I don't think people on either side are "wrong"; they have differing tastes, so let's try to keep the recriminations and snark out of this, yeah?
It's true that sticking to the relatively mundane makes balancing more difficult, but it's not insurmountable. For example, in 1E Fighters had better saves than wizards of the same level in most cases. ("Enduring...through sheer force of will" is the justification given for fighters making saves in the DMG, if you're wondering.) Only fighters (and rangers and paladins) could get the full HP benefits of a high CON or (if they were lucky/cheating) have percentile strength. And only they could eventually attack twice per round.
I might suggest, for example, rather than stopping wizards from casting meteor storm, placing more limitations on casting it. Suppose most spells take at least a full round to cast (meaning it goes off at the beginning of your NEXT turn); Meteor Swarm might take 2 or 3. Any damage taken during that time has a chance to interrupt the spell, not only making the action wasted, but also wasting the use of the spell, and having a chance to trigger a roll on the Spell Mishap Table. Perhaps make it more difficult to learn new spells, especially high level ones, with scrolls and spellbooks of that level difficult to find and requiring substantial research otherwise.
*In a sense, Batman can leap much higher than a normal person--using a Batrope. He can glide. He can repel sharks (
https://www.youtube.com/watch?v=XJlHjf_E--4). He's also probably at least partly a rogue or something, but that's beside the point.