While you make fundamentally good points, I think there is a core reason that balance is important to me: DnD is a multiplayer game, not a singleplayer game.

I actually think it’s fine that different classes are strong at different levels! The entire premise of Wizard is that they’re a squishy who will die if they’re sneezed on at level 1, who grows into a reality-warping god by level 20. Having someone that needs to be looked after at low levels and can then look after the team at high levels encourages teamwork!

The reason that I say DnD is so badly unbalanced is because once level 5 comes around? Casters very, VERY firmly become way better than non-casters for two reasons. Casters have AoE damage, and casters have utility. Non-casters have no utility, and because they also really struggle to increase AC, they can’t function in any role except for single-target damage. A good level 5 caster can make the rest of the party feel really lackluster because they can do in one turn what the rest of the party needs 4 or 5 turns to do (HP and AC are much less of an issue at this point too). And this gap only gets wider and wider with every passing level, which rapidly makes it less and less fun to play a non-caster.

Once level 13 hits, anyone who isn’t a full caster is completely irrelevant. That is not fun for anyone who isn’t a full caster. Hell, it’s SO badly broken at this level that it’s almost certainly the reason why Baldur’s Gate 3 only goes up to level 12- and that game already does a huge amount of buffing martials and nerfing casters. A 13th level caster can instantly beat pretty much any encounter not explicitly designed to bully them, and even then there’s a good chance they find a way to solo the encounter on turn 1 anyways.