I’m pretty confident that demi-human level limits, at least in AD&D 1st edition and onwards, never worked effectively to balance demi-human powers because the experience point system was rigged to ensure that multi-classing as a demi-human was massively unbalanced. I am writing this theory out by memory, and I’m aware that it has been done over a bit in other blogs recently, but I can’t find any discussion of the effect of the early incarnations of the xp system on multi-class PCs. I recall when I was playing AD&D back in the day that I became acutely aware of the imbalance in the system pretty quickly, but it hadn’t occurred to me for years since I played it, and I’m going on my memory of the advancement tables in writing this post so I may be completely wrong, but here goes…
Level advancement in AD&D was basically geometric, so for example you needed 2500xp to get to 2nd level, 5000 xp for 3rd, 10000 for 4th, etc. The amounts required doubled each level until about 12th, though there were a few levels in the middle where some classes went up in an arithmetic fashion, the most striking being (from memory) wizards, who between 6th and 9th level didn’t double in required xp. Multi-class characters required twice as many xps to gain a level. The big upshot of this is that a single-class character will, for the majority of the game, be only 1 level higher than the two classes in a multi-class character. For example, you could be a 4th level human fighter for the same amount of experience points as you could be a 3rd/3rd level Dwarven Fighter/cleric. In general, though, the benefits of these levels are essentially additive, and the natural assumption most people make is that a a 3rd/3rd level multi-class character is closer to a 6th level single-class than a 4th level single-class.
This means that until about 9th level (roughly when the geometric advancement stops) a multi-class character will be approximately twice as powerful as a single-class character. A triple-class character will be even better – a 5th level single-class fighter would be roughly equivalent to a 4th/4th/3rd level fighter/cleric/thief by dint of this geometric progression. Once the characters reach (about) 9th level this distinction stops, and the multi-class characters go up in levels at the same rate as the single-class characters, so a 15th level fighter would be (roughly) the same as a 12th/12th level fighter/cleric.
Demi-human level limits serve to “balance” the extra powers of demi-humans by stopping them from achieving epic levels. But consider even harsh limits like those on a halfling fighter/cleric (roughly 7th level and 6th level, I recall). The halfling fighter/cleric will reach this limit when a human roughly reaches 8th level. In order for the human to gain a numerically equivalent set of levels they will have to adventure for another 5 levels, i.e. the human remains weaker than the halfling until 13th level. For an elf magic-user/thief with good stats, the elf can probably reach 11th/10th level, so from 12th level until 22nd level a single-class human will be underpowered relative to this elf. Given most campaigns never reach 20th level, but the power imbalance starts at 3rd level and just gets worse until 9th level, this is a pretty blunt and ineffective tool.
I think D&D 3.5 fixed this by making the level progression arithmetic and making multi-classing possible for everyone. This is a much more effective balance on the power of demi-humans than giving them level limits which occur too late to practically affect the most significant problems, and probably never become practically applicable for the majority of parties.
I’d like to add the disclaimer that this post is based on my memory of a game I haven’t looked at in maybe 15 years, so any mistakes in the content should be seen as speculative revision. I recall being really vexed by the simultaneous problem of demi-human level limits on the one hand, and overpowered multi-class characters on the other, and I may be wrong in all the particulars. A lot of beer has flowed under the bridge since my last chaotic neutral magic-user thief freed the prisoners and killed the ogre…
fn1: in terms of THAC0 and hit points it wasn’t, but in exchange you got to start the campaign with spells and combat powers. So a 1st/1st level fighter cleric was basically a cleric with better THAC0 and hit points than a cleric; or a fighter with 1 less hp (on average) and cure light wounds. A 2nd/2nd level fighter cleric has the THAC0 of a 2nd level fighter and but has the spells of a 2nd level cleric. This fighter’s single-class comrade will be a 3rd level fighter, so his/her THAC0 will be one better and he/she will have 1d10+2 more hps on average. At 7th level, this fighter has 7d10 hps (mean 38.5 hps) and a THAC0 of 14, with no spells. The 6th/6th level Dwarf has 6d9 hps (mean 30hps), a THAC0 of 15, and the spells of a 6th level cleric. I’d rather play a character with 8 less hps (on average), 1 higher THAC0, and about 7 spells, as well as undead turning abilities, personally. There is almost 0 mechanical advantage to any other choice. And I think it’s even worse if you play 3 classes, because the reduction in hps and THAC0 is negligible but you gain all the 3rd classes abilities. The classic would be a cleric/magic-user/thief, so you get double the spells of a mage, and better THAC0 and hps than a single-classed thief with the same xps.