I think they do, and as you mentioned you can explicitly remove such a restriction. Sets and types are once again two different kinds of objects in mathematical theory, and a set-theoretic type doesn’t seem to be based either on set theory or type theory.
Sets and types are foundational mathematical concepts so I’m looking for how elixir’s types fit in that context. Union and intersection are not something that belongs only to sets.
Unions, intersections and negations are available in types as well and are by no means exclusive to sets. The distinguishing feature of a set vs type is that a value belongs to just one type while it can belong to several sets.
They didn't "test" the concept of infinity. They said that the results of the infinite monkey theorem are well known, and they wanted to see what happens in the finite case.
This is a misunderstanding. All the energy in our « observable » universe was compressed in that small size. We do not have any estimates of the size of the actual universe now, nor at a time shortly after Big Bang. For all we know, the universe might be infinite, both now and back then.