Sure, but you'll then have to just do the same thing some other way. There is sure to be the guy who wants to play a sword-wielding caster, or a wizard with a bit of a talent with a shiv, etc. There is a HUGE difference between 2e-like MCs where the MC is really effectively a hybrid class, and 3e MCing which is effectively a classless template system. The former adds some flexibility to character creation, the later annihilates the very concept of class and makes it virtually meaningless.
So yeah, if you are forcing me to choose, none is better than ala-carte, but that's not an argument against doing it 2e-style.
My argument is not against the 2e-style but in favor of 3e-style because it actually
includes 2e-style but also allows more.
If you go back to 3.0, notice how the multiclassing penalties look: no penalty if all your classes are max 1 level apart, penalty if they are more than 1 level apart (except favoured classes). This is clearly inspired by 2e multiclassing, dividing your XP equally (in 3e cannot be
exactly equally since you take levels separately, but as equally as possible) gives no penalty, so this was the reference multiclassing they had in mind. However they also allowed
other combinations with unevenly spread levels, in which case there were some penalties because they were predicting that some combinations were going to be better, and that actually turned out to be true... in general, a 3e martial class with a couple levels of spellcaster (or a spellcaster with 1-2 levels of a martial class) worked better than a 50/50. Unfortunately it also turned out that the former is generally quite enough on par with a single-class PC, therefore it shouldn't have had multiclassing penalties at all, and the latter is generally subpar even at no penalty.
However, the main reason why the latter is subpar in 3e is IMHO the fast scaling of BAB, ST and spells DC, so that giving up more than a couple of levels of spellcasting or more than ~3 martial levels, already makes you lag behind in numerical terms.
Bounded accuracy should be able to significantly reduce this problem, so IMHO it's definitely worth to check how 3ed-style multiclassing would work on top of 5e!
It's the best choice for first attempt really, then if playtesting shows that it's not good enough, we'll try to come up with another system.
But if it does work, it covers a lot of ground in terms of possible characters, including all 2e-style multiclassed characters. It probably doesn't cover 4e-style multiclassing, but IMHO it is definitely possible to
also allow that in the game, with a separate rules module that can fit in 1 page.