No, it is perfectly balanced. It just is terrible game.
See, that's why I find the definition of balance that includes
maximizing player choice more useful that whatever unstated definition of balance you're using that deem a terrible, choiceless game somehow 'balanced.'
What is that definition, BTW?
I simply don't agree with your definition of balance. Yes, having multiple choices is good game design, but that is not balance.
Thus the requirement those choices be both meaningful and viable.
A game with three equally viable choices is just as balanced than a game with 78 equally viable choices.
I mean, the latter is /better/ wouldn't you agree?
The latter is probably a batter game, but not because it is more balanced, but because it offers more agency.
A better balanced game will tend to offer more agency.
Yet the cost it took to get even there was too much for many. So why was this sort of balance important again?
The cost of balance is less imbalance, honestly. Complaints about 'how a system is balanced' typically boil down to some of the choices seeming less meaningful - which means it's not actually as well-balanced as it could have been.
It simply limits what way you need to run the game if you desire balance. And you must always balance around some assumption.
If you layer too many restrictions on a system to 'balance' it, you're effectively reducing player choices again, which means you're not balancing it, you're just working with the imbalances it presents. It's similar to taking an imbalanced system with a number of non-viable choices, and just excising those choices. The result is a smaller game that wastes less space and avoids offering 'traps,' but it's still not any better-balanced, because it isn't providing any /more/ choices that are both meaningful and balanced than it did before.
That's another thing useful about this definition, it recognizes that banning or otherwise removing choices is not as good a solution as fixing choices that are non-viable or render other choices non-viable.
I don't think there can be RPG that is balanced regardless of how it is run, that nonetheless can be ran on myriad different ways, unless you homogenise the characters massively.
Making choice of character meaningless would be self-defeating if you're trying to get a better balanced game.
Perfect balance, is impossible, of course, so trivially it's true that you cannot balance a game for an infinite number of possible ways it might be run.
But improvement is always possible. 5e, for instance, might be balanced in a game that consisted of little more than time-important, 6 or so encounter 'days' consisting almost entirely of combat vs enemies the party outnumbers. That's /very/ narrow. Balance in every conceivable campaign might be unattainable, but balance in more than just /that/ is not too much to ask, indeed, balance in the mode of play surveys show to be the most common 1-3 encounter days, would seem prudent...
The characters will have capacities usefulness of which will depend on the situation they find themselves in. So in effect the "power" of the character will be different depending on the frequency of situations that their capabilities are optimal for.
With 'viable' as the bar rather than optimal, that's not an impractical thing to work towards. D&D traditionally fails very badly at establishing any sort of balance across campaigns with different emphasis because it makes some classes very flexible and others more highly specialized. Fighting Man and Thief, very specialized, Cleric, less so but forced into healing primarily, Magic-User as flexible as his spell list. Casters in general and wizards in particular have become ever more versatile as the game evolved ("changed slowly over time," 'k? Developed. Whatever), while non-casters have at times become even more specialized.
Classes (if a game goes with them at all) can be differentiated without being given functions so limited and inflexible that they might sit out sessions, or theoretically, even whole campaigns. When they aren't you have "the netrunner problem" which, of course, is a failure to balance classes....