Why is UUID an overhead? Not the generation of it, right?

I was thinking about the generation indeed: it needs entropy.

Is that the load of all rows?

Sorry I didn't understand this question.

Isn't it the same problem for Set?

In a set, the tuple representing all columns represents the primary key as it's unique.

But I think the more important thought is that if you have a Bag, ORM will need to load all elements anyway so there's no benefit at all in mapping such elements on separate "rows". So we could make it mandatory to store such a collection as an embedded collection (like I think a user would store a bag in Protobuf..) and not give the option of separation.