My immediate thought is the same one I usually have; limits can be very good. Limits define our experience, and make it better.
To put it in more concrete terms, the best definition of an adjective I have ever seen was that an adjective is a word that limits a noun. You can have any kind of box, but once you have a red box, it can no longer be blue, or green, or yellow. Once it is a big box, it cannot be a small box, or a mid-sized box. And so on.
Specificity is the soul of narrative, and while adjectives limit nouns, they also define the noun; it is only through limits that we truly can be engaged.
This gets to the basic D&D experience; for better or worse, D&D uses classes. Classes define the D&D experience. Classes are one of the primary limits within the game, one of the primary points of differentiation. A wizard is not a fighter. Allowing an a la carte system (as you have in some other RPGs) would be a fine gestalt approach, and maximize freedom, but would also essentially remove the class system.
Moving from the abstract to the more concrete, there is nothing wrong with your proposal, per se. If anything, it points to an issue with 5e; 5e mimics the traditional class structure of D&D, but the classes themselves (esp. when combined with a la carte backgrounds, feats, subclasses, and multi-classing) do not really have the same amount of meaningful differentiation as a class system should provide. But, by the same token, it doesn't have a true gestalt option.
So it's trapped midway between true freedom and meaningful restriction.