Yep, multiclassing has been a problem for as long as I can remember. It's better in 5E than it has been for a while, but it's still...
...well, let's just say I'm glad it's optional. How would you tweak 5E to fix multiclassing, assuming all subclasses are gained at 1st level?
Honestly, I'm not sure how I'd change multiclassing. I'm not much of a fan of the mechanic anymore. I just don't think it works very well as a concept. You can try to fix it, but I think the best solution to a-la-carte is called GURPS. That is to say, it fundamentally doesn't work.
One simple solution would be to adopt something like 3e favored classes, but not in the way most people remember them. Instead, the rule is: you can only increase a level in a given class if no other class you have is lower level. For example, if you're a Fighter 3/Wizard 4, when you reach level 8 you
cannot gain a level of Wizard, because Fighter is lower level. You'd have to wait until level 9 when you're (presumably) a Fighter 4/Wizard 4. If you then took a level of Rogue, you'd have to wait until you got those levels equal before you could take anything else.
The drawback, of course, is that adds a severe hindrance to multiclassing, because it assumes each class level is of equal value. That's not true. Fighter 5, Fighter 11, and Wizard 5 are phenomenally more powerful than many other levels. The devs knows this already -- it's not a secret -- which is why they don't frontload levels 1 and 2 as much. However, this does mean that such a character needs to get to level 9 before they can get one level 5, and that's not worth it. It's too high of a cost. Even AD&D knew that, and that was when character levels didn't do very much of anything at all.
There are other simple solutions. You could apply a cumulative -1 penalty to the character's proficiency bonus (to a minimum of +0) for each class beyond the first. The drawback is that it has really weird side effects on incentives the more that you think about it. You could say that when you multiclass away from a class, you can never return to it. The drawback is that the
really abusive builds aren't affected by that at all.
The other option is to invent something more complicated. A special multiclass class, or nuanced rules for abilities. The drawback there is the complexity itself. Multiclass rules are already fairly simple as possible solutions to the problem, but they're still one of the most complex rules in the whole game.