The balance issue is generally within the party, and it is less to do with survivability and damage output, and more to do with everything else that the party might try to do during the sessions.There is one pivotal assumption underlying all of this "the game breaks down" argument that keeps resurfacing that is, in essence, complete bull%!#$.
The assumption: That balance is a huge concern at high levels. It is not that important.
D&D is an RPG. A role playing game. Characters play a role in a story. In D&D, a high level character, especially if it has been played since low levels, has been through a lot. They struggled against goblins. They foiled capers. They waged war on giants. They traveled the planes. Now, at the highest levels, they can achieve amazing things and only the mightiest of the foes in the land can really threaten them. Because they are not just heroes - they're super heroes.
Things that challenge them in terms of survival should be the exception to the rule, not the rule.
"But that would be so boring!"
No. I did not say nothing should challenge them. I said nothing can threaten them.
Good high level play is often about stakes that are external to the PCs. Protecting the land. Stopping the curse. Give the players objectives that can be achieved or failed without threatening the lives of the PCs. When you play that game, balance which focuses on the height of power levels, is much less important than the breadth of powers and capabilities.
Take the Fighter: outside of rolling attack and damage during combat, there is little else that the class provides above the baseline out of combat. Compare to the wizard who gets the same baseline (skill proficiencies) and also a wide range of other capabilities in the form of spells, which can be used as imaginatively as the DM will allow.
At high levels, even the very baseline: of the fighter class: ability checks are substandard compared to the wizard and many other classes. The situations where the Fighter can be expected to shine: Athletics and other physical challenges are generally now easily bypassable by spells, whereas the wizard's knowledge checks remain relevant and useful.