The first main problem is that in a system of exponential growth, you're trading the highest-level features of one class for the lowest-level features of one or more other classes. This is most notable with spellcasters and, in 5e, the difference between high-level spells and low-level spells being upcast in high-level slots.
The second main problem is that it's practically a tautology that the defining features of a class need to come early because... they're the defining features of the class, members of that class need to have them. But then, it comes too easy for members primarily of another class to get those features by taking a short dip in the class... and then the designers start spreading those features out and pushing them up to higher levels so that single-class characters don't really "come online" until higher levels, and multiclass characters can't get those features without trading even more of the highest-level features of their class.
It adds up to a system that can only produce unviable, underpowered characters when practiced as intended, and playable-- balanced or overpowered-- characters only through exploitation of unintended and overpowered rules interactions.
I've also got a subjective complaint, that I just can't wrap my head around how a character can stop getting better with the class features of a class that they're using every day.
The AD&D rules were a clunky mess, but they were more or less functional for portraying a character who was more or less two or three different classes. The first set of Fourth Edition rules, the feats, were personally unsatisfying; the second set, the hybrids, were better but fell down on account of the way classes intersected with the ability scores. Sort of how 5e multiclassing only really works with the Charisma-based classes.