I like them.
Sorry.
I've listened to the arguments about 'why don't single-classes have prerequisites too?'. My counterpoint is that they'd be largely redundant. The used to include prerequisites for all Classes - Fighters used to be required to have a minimum Strength of 9, ditto Rogues for Dexterity. But honestly, what's the point if you have points spend at character generation anyway? If a player deliberately chooses a low strength Fighter, or whatever, then it's down on them.
Multiclassing is a different issue, however. Players who want to shift Classes after starting play need to be able to justify it both in game terms and narratively. A character is very unlikely to shift Classes unless he shows a clear aptitude for the role - which is represented by the Ability score requirements. I would argue that there also needs to be a mechanism, possibly, for shifting character traditions, paths, etc, within Classes however.