I also do not see why (a,a) could not be a container of exactly two elements, as opposed to current GHC which insists it is a container of exactly one element. (Case for the mental institution, I'd say.)

Because this isn't how types in Haskell works. `Foo a a` always parsed to `(Foo a) a` and no instance of any class can implement it differently than `(Foo b) a`, unless you want to throw parametricity out of the window. This has been long before `Foldable`.

Best regards,

Marcin Mrotek