It gives you the opportunity to play as a different character, but it doesn't change how you actually play the character that you end up with. You're still limited by what the character can do, and whether those capabilities are pre-determined or customized from a million different options is irrelevant to the quality of the game.
Even if you're playing a basic game with four classes and no multi-classing, you can still get the full game-play experience out of that. A multi-class character with feats isn't inherently better or worse than a single-class character without feats, as far as playing the game goes, but it is inherently more complex and requires more work to make. So given that there's a cost associated with that complexity, and no real benefit in terms of game-play, I don't really see the appeal to this model of class design.
The benefit, IMO, is that I can play what I want. Instead of a multitude of abilities in my main class that are "Almost, kind of, what I want", I can mix a couple of classes and get a character I actually want. Now, they could make a bunch of subclasses for the base classes, that represent the multiclassing, but that just sounds silly.
I currently have a character that, if I were to play him to 20th level, would be Rogue 8/Warlock 12. Are they meant to have a Warlock subclass that represents the Swashbuckler I get from rogue, as well as the sneak attack damage to go with it? Or a Swashbuckler that pulls in some Bladelock? Both, for people who want more Swashbuckler or more Blade-lock? That sounds way more complex than just being careful to not front-load a class too much.
I have had exactly one character that I thought of that only requires a single class. If you gave me a choice between simplicity or customization, I would choose customization every time.