But then shouldn't we expect similar stuff to happen for rabbits? for them to evolve away from the primordial shared cuteness criteria?

They may have. Just not as much.

Shouldn't more helplessness, more (and longer) dependence on adults result in stronger perception of cuteness of them? (via shifts in their appearance and our criteria)?

I don't think the reason modern humans take care of their children is just about how cute they are. We've developed additional instincts to encourage child rearing (cultural pressure, some more specialized attachments that individual parents have with just their children and not with other cute things). This is what I mean by the function being fulfilled by another feature. This isn't evidence of anything in particular but cuteness feels sort of cognitively primitive, doesn't it? Like fear? I don't know if associating qualia like that is a permissible inference.

I've actually ranked this hypothesis third behind "Babies are cuter after all." and "Coincidental superstimulus".