The demihuman level limits are there to enforce AD&D's human-centric genre of sword & sorcery fantasy. AD&D assumes lots of self-interested adventurers running around the fantasy world, the most successful of whom will eventually become the region's local lords, patriarchs, wizards, and other rulers. (It also assumes that a given player might by running any number of characters, so having your non-human PCs suddenly hit a ceiling is no big deal — when that happens, you just keep on running your human characters for the high-level, dominion-ruling or planes-hopping adventures, only brining a demihuman out of semi-retirement when the evening's adventure is a low- or mid-level caper in need of that demihuman's unique talents.)
But if you take away the level limits and class restrictions, humans have no advantages at all, and so the players will always play demihumans — which in turn means that the game-world will eventually be ruled by high-level demihumans, lording it over the human masses. It raises the question, why weren't the demihumans already in charge before
PCs started running around and getting powerful?
(And the idea that it doesn't matter if the makeup of the PC party doesn't reflect the population of the game world, because the PCs are already outliers by virtue of being adventurers? That idea makes no sense in the context of an AD&D campaign, where it's built into the very foundations of the leveling system that gaining experience also advances you through the ranks in your character's
society. Adventurers in AD&D are emphatically
not outliers and fringe elements.)
That's the underlying logic, at any rate. So, to the question at hand: (1) are the multiclass combinations too good to allow unrestricted? and (2) what can we do for humans if we give their best two advantages to
everybody?
It's easier for me to answer (2) first, as the 2e DMG already offers a great suggestion. If you're going to let demihumans pick any class and rise to any level, they have to pay for their other advantages somehow, and it has to be heavy enough that humans are worth considering (but not so heavy that demihumans
aren't worth considering). The 2e DMG suggests making nonhuman PCs in such a campaign earn double the normal amount of XP to level up, and this works well enough given that the XP tables are exponential until 8th or 9th. A single-classed demihuman will be one level behind a single-classed human (at least until name level, when they begin to fall further behind). A double- or triple-classed demihuman will advance quite slowly, and it'll hurt a bit, but it won't feel untenably glacial until after name level.
Don't allow multi-classing within the same class group. Many years ago I once allowed a MU-Illusionist multiclass and came to regret it mightily.
2e, at least, is explicit about that being illegal. 1e didn't really need to point it out, because the sub-classes
were examples of their class group. If an illusionist
is a magic-user, and a magic-user/magic-user is patently absurd on the face of it, there should be no need to explain to players why a magic-user/illusionist multiclass is nonsense.
(2e also helpfully slots monks neatly into the priest group and bards into the rogue group, so you know where all the classes go. There are only ever five groups — warrior, wizard, priest, rogue, and psionicist — which handily limits the multiclassing and dual-classing possibilities.)