The way I'd heard it all kinda makes it seem like Wizards need to keep their distance even at high levels due to being kinda insanely fragile, wheras Fighters at high levels can just wade into monsters and start swinging.
Nope. Fighters are actually pretty poor at defence. You can optimize a melee character to be near invincible. I actually had one 'Wolverine' build idea but that's more Changline Totemist 2/Barbarian 1/Crusader 1/Warblade 1/Warshaper 4/Witch Slayer 2. Still a melee combatant, but he's much more effective at killing things and he can regenerate most of the damage he takes, assuming his foes get a shot in. But that requires optimization, and you'll note it didn't contain a single level of Fighter, despite being a fighter.
As for the Wizard, they'll be fragile at low levels unless specifically optimized for low level survivability. But once they get to level 6 or so, they can start keeping up defensive spells for long periods of time. They still don't want to get hit, but it's not as big a deal as it was.
At level 9, a Wizard can start flying 24/7. By level 10-12, a Wizard can have redudant defences up all the time.
Now Wizards will still want to keep their distance, but that's just because why risk it? They can polymorph into a Hydra and melee it up if they want to, but it's easier to just blast people from 200 feet away before they ever even get a chance to act.
And of course, at level 17, spellcasters ascend to godhood, as mentioned previously.