Hiya!
I don't think the rules require the DM and Player to make the training an aspect of the narrative. That's the problem. Well, one of them. What is more annoying is that MC is listed as OPTIONAL, yet AL uses it. Same goes for Feats. But that's another thread.
This is "fluff" and "DM/Player style"...not the rules for MC. Oh, sure, ANYTHING can be "retroactively applied/assumed". I don't like that. I don't want to see a player suddenly say "I added a level of Wizard. I guess my Fighter was hitting the libraries, and taking night-class at the Wizard Academe or something"...because that is simply not what "happened" during the X number of sessions. It's the same as if the DM said "Oh, yeah, you guys did destroy the Bad Evil Dude's castle and burn down all the surrounding farms supporting it. But I guess he was just rebuilding it and stuff over the last couple months"...when the PC's never left the town that is within sight of the hill where the Bad Evil Dude's castle was...and now his new one is. It's lame, it's cheezy, and it's rubs me in so many wrong ways.
I don't think your individual class-skills hold water though, for this debate anyway. A Sorcerer did/does have "sorcerer points" at level 1...he just doesn't know how to use them yet; he's still learning how. The Rogue, the same thing...he just didn't quite "grasp" how to do this or just wasn't good enough at it. A class doesn't just "poof!" in knowledge of his abilities...he just isn't experienced enough to use the correctly or at all. Hence...XP and Levels.
^_^
Paul L. Ming
So, to you a spontaneous set of points or new speedier movemt options and maneuvers for action they havent taken is fine as long as its not wrapped up in different class name.
Gotcha.
My point with training wasnt about retro fitying the entire last month of play. You keep creating conflicts as problems but thebproblems are not required by the rules.
Most games i have ever sern do not assume every bit of character time is played out or even announced on screen. They dont announce every piss or training workout or meal.
So, some GM and players are fine with "the next level stuff was done off screen". Some might actually prefer referencing it in various ways as part of side fluff as the level is played up to. (I frequently see that more for mystic side.) Some might prefer more exacting insertion and can apply various training rules for things.
These can apply for MC or single class or any conbo of things.
But your examples of "we choose to do it this way" and "it bothers us" are examples where the rules chosen and the preferences clashed, not examples of bad rules which force you to do things you dont like.
Edit to add actual case in point not hypotheticals -
In my 5e game my halfling sorc dreams of dragons, thinks she she talks to dragons in her dreams, uses dragon decks to tell futures for money and is an entertainer who sings and dances and plays the flute.
She will be working with the bard on performances and spending time jamming studying watching listening etc.
So, at sixth level i plan it likely to be the case that she takes a level or three in either warlock or bard MC.
Which ever way it plays out, i have no idea, decision will be made based on the first four levels events, i will have in game examples all along to make that transition fit the narrative seen in play to that point.
It will be a turning point for sure but not shocking or unprecedented.
"So, those voices were real?" Or " she picked up metging song and her innate gifts?"
Was this required, nope. But since i prefered it, i chose to do it so i wont have any jarring back story retrofit or inexplicable swings.
I plan to make my decision when i reach 5th so i can give my GM a full level of play notice, especially for the warlock route if i choose that one.
Its basically "it hurts when i do that so i dont do that" thinking. You dont need rules requiring rolrplaying to roleplay the stuff you think should be roleplayed.