I've never planned a 20 level path, and this is my method! But I do understand what you are saying, and I actually agree: characters should evolve through game play and they are far, far more than their backstory. Where I think we differ is in the degree of that evolution. As I mentioned, the classes supposedly represent years of previous training and experience. One does not just wake up one day and become a wizard when they've spent their whole life as a thief. So for a character to "suddenly" gain levels in wizard doesn't work for me. There has to be a connection. So with that in mind, we have a few options:
1) The character doesn't become a wizard. But that thief might dabble into the mystic arts as an Arcane Trickster. In this case, it's simply a question of archetype selection. As I think I mentioned in my first post in this thread (or maybe it was a different thread), the 5e archetypes largely remove the need to MC since they emulate many of the traditional MC concepts. This is my preferred method. Microevolution, if you will.
2) The characters take a year or so of Downtime, with the PC using that time Training for the new class. Then they can MC into the new class. Now this only works if the players are all willing for their characters to have that extended downtime. Personally, I don't think that's necessarily bad. Pendragon did great things with the passage of time and it's direct relationship to the characters' developments. Slow evolution.
Or there is the option posited above...
3) Connect the MC with the character's backstory so that there is a reasonable expectation that the base for the class existed, so the years of downtime are not necessary. Hidden evolution.
And actually, now that I think of it, you could argue for option 4, which allows certain classes to be overnight MC. Warlock comes to mind. Theoretically, a Patron could overload a character's mind with all the knowledge and understanding necessary to be a Warlock 1 as soon as the character seals a pact with them. But this method really only would work with select classes. Cambrian explosion?
This is also why I am not a big fan of MC. Now - and I don't want to be misunderstood - in my experience most players have a general idea of the character they want to play from the beginning. They typically know if they want to be a tough guy, a sneak, a spell-caster, or what-not. Further, they usually know if they want to do a "spellsword" or "magician thief" early on. So -still speaking anecdotally from my own experience- most (though not all) of the people I've seen who "spontaneously" MC in a direction that has no connection to their character's backstory or no direct connection to the adventures they've encountered are just making a grab for new and kewl powerz. While this is obviously not true for every player, this sort of macroevolution does seem to attract that sort of player. So it is easier and more consistent for me to just disallow most MC, and demand a tie in for the ones that are allowed. Does this punish the "good" players who aren't looking for a power grab? I suppose, if you consider the class/sub-class combos to be too limited and hence punishing. But in my estimation, the class/sub-class combos cover most "normal" MC combo concepts, and are good enough.
I wouldn't advocate this as a universal rule that must be written in the books and applied to all tables, but it is definitely the preference for me at the tables I game with.