> And if someone builds a pure tower that goes int32, double, complex, quaternion, do you think that's inherently self-defeating because it can't live up to the promises of a tower?

Assuming the obvious implementation of complex and quaternion built on two or four doubles, it's fine. Each type represents a set that is a proper subset of the next type in the list.

Annoyingly, it'll all go to crap if you have int64 though.