Multiclassing for Demi-humans in AD&D worked so much better from an optimization standpoint. Not necessarily a narrative one. And it didn't work for humans.
I like the modern version of it because it allows my character to grow and explore things in the fiction of the world and have it meaningfully represented on the sheet.
I'm playing a Fighter (EK) in a game right now. I never planned on multiclassing into warlock, but in our game, we've traveled to the fey courts, and my character has been noticed and contacted by the Raven Queen, or maybe her agents. If I decide to pursue those threads, I can very easily see multiclassing into Warlock because of the story.
Certainly, I couldn't have done that in AD&D without DM fiat or something.
I find multiclassing both over and underpowered.
depending how you do it.
1-2 level dips can be problematic if you count lets say levels 10-12.
2/9 split can be more powerfull than single class 11.
I would only allow equal split MC. that is 2 classes must be within 1 level of each other.
but 6/5 split is usually a lot weaker that single 11 or 2/9 split.
so solution is that MC should have more "effective" class levels that single class, but only with even split of levels.
In my variant dual classing, you can MC only with 2 classes, and you must keep classes within 1 level of each other.
But, you get extra class level on character levels 5,8,11,14,17 and 20.
that is if you are 4th level MC fighter/wizard you are fighter2/wizard2, but on 5th level you are fighter3/wizard3. On those dual levels you take average HPs and average HD for healing.
In case of fighter/wizard you would get 5 HPs (6+4)/2 and one d8 HD(middle of d10 and d6).
and for all other mechanics you would be counted as 5th level character, not 6th
then at 8th level you would be 5/5 split, 11th level would be 7/7, 14th level 9/9, 17th level 11/11 and 20th level is 13/13 split.
on average 13/13 dual class gives same number of HPs and standard 10/10 fighter/wizard split, same proficiency bonus, same number of HD healing, same weapon/armor/save proficiencies. It just gives extra 3 class level feature of each class.
you also get your features at much slower rate, 8d6 fireball at 8th level is a lot weaker than at 5th level and fighter 3rd attack at 17th level is also very late.