Existential subtyping as generic constraint

Exactly. If you want to apply the notion of existentials to types, it would be applied to generic types (i.e. type constructors) and we would have things along the lines of any Array. This same notion would apply to classes.

Do you know of any OO language which has such a notion? Do you know of any use cases for it? It doesn't sound like something that would be useful to me.

This is why I said upthread that we wouldn't be able to use existential subtype constraints without introducing the any syntax. I think it's rare that an existential subtype constraint would be useful anyway so I don't think it matters too much that we are currently unable to spell it.

What do you mean here? IMO, the any AnyObject syntax is clunky and confusing to the point that it might be enough to warrant deprecating AnyObject and replacing it with Object, which is already considered a bit of a wart.

Why would we want an existential in the latter case? It seems to me that importing language support for variance would be the more productive path there.