I actually played 1st ed AD&D in the 90s, but yes, we followed the level limits. Considering that most of the demi-human races were quite powerful we felt it was reasonable enough. That and our campaigns never really got beyond 10th level.
Demi-humans could mutliclass, they had racial abilities/immunities/special powers, you got ability score modifiers that you could use to your advantage. On the one hand, a demihuman at level 1 was usually more powerful than a human at level 1 (humans getting no special powers per se), on the other, eventually a human could outstrip the demihuman in power through class levels. It was an even trade-off I thought.
If you were to take away level limits, you would have to give humans something, because otherwise there would be absolutely no reason to play a human unless you wanted to be a paladin or monk.