I think it's to avoid the wild multiclass dipping you had in 3.5. The lack of ability scores requirements, combined with the basic mechanic of gaining +x on saves, bab and whatnot, allowed to create absurd but OP combinations (by dipping appropriately you could have far better saves than any other class without sacrificing too much).
Besides, it kinda makes sense that you shouldn't be a Wizard if your Int score is 8... There shouldn't be multiclass ability score requirements IMO, but class ability score requirements, like in 2E. The problem with this is that you may restrict too much the concept of a class, so you'd have to multiple alternative requirements, probably negating the point entirely.