D&D is not a technical game like chess where it’s all about equal chances, because these are for games that you are playing to win. As has been said as early as in Basic, but which has been repeated in all (good

) editions of D&D since then, D&D has not been designed to be won, just to be played and enjoyed.
So for me, the only balance which is important Is not technical at all, it’s about allowing all your players, including the DM, to have fun while playing the game. And recognising that different people have different views about what is fun in playing the game, we all have different tastes.
And this shows why technical balance is ultimately irrelevant, so many factors come in to impact it that, even if it was perfectly designed, it would have little bearing on what matters in the game.
Of course, if you play a very technical game, with a heavy focus on combat, and where the fun of the players comes mainly from overcoming technical challenges (I’m not making any judgement here, it’s as valid a way of playing the game as any other), balancing the combat and the capacities of the players might seem very important, but in the end, it all bows down to other types of balance which are not inherent to the system, but to the circumstances. For example, if the encounters are designed in a way that always favour certain types of approach, or certain ways of gaming, it will disturb the balance of the system. Or the tactics of the players might influence it. Or their preferences in terms of play. Or their inherent capacities. Or what kind of items they find during the game. Or the relationships that they develop with NPCs, and the reactions of the later.
And I’m not even mentioning the fact that I’ve never met a group that was as single minded as the above, when you take into account all the other elements that contribute to fun for actual tables.
So 5e made exactly the right decision, to have a game that is not completely unbalanced, but recognising that not only would it be futile to spend too much effort on this, but that previous efforts in that direction resulted in editions that were in the end not even more balanced (3e, I’m looking at you), or editions where the need for technical balance caused the rules to “severely limit what characters can do, which would be counter to the open-endedness of D&D”, in the designers’ own words, which I fully agree with.
So just balance the fun that your players are having using all the incredible means at your disposal as a DM, including the rules if you need to, it realising that they are just that, one of the many many tools, not an aim in itself.