This must be why kinds (types of types) in Haskell are a separate and less powerful thing than ordinary types?

I believe it to be historically true, but Dependent Haskell might change this (https://ghc.serokell.io/dh see unification of types and kinds).

In Lean (and I believe Rocq as well), the Type of Int is Type 0, the type of Type 0 is Type 1, and so on (called universes).

They all come from this restriction.

	▲	aureianimus 2 hours ago \| parent [-]
		With respect to Lean/Rocq, that's true, with the subtle difference that Rocq universes are cumulative and Lean's are not.

amelius 4 hours ago | parent | prev [-]

I suspect not, because in that case Type is not a Type itself, but a Kind.