I'm wondering if treating type[a|b] and type[a]|type[b] the same actually makes sense and even if so, whether union types should be supported for type[...] arguments at all:

E.g. if we have a single-dispatch function with an implementation for type[a|b|c], wouldn't people expect to be able to pass e.g. a|b to it and have it dispatch to that implementation? That would be much harder to implement than my current naive implementation of just splitting up unions into their individual constituent types, especially considering issubclass(a|b, a|b|c) isn't even possible.

So maybe unions of type[...]s and type[...]s of unions should just not be allowed for now, deferring them to when (if ever) issubclass supports these kinds of checks (or Python gets another issubtype function).

OTOH, it's unlikely that introducing support for dispatching to type[a|b|c] given a|b later on would be much of a breaking change... If only dispatching on single types is supported for now then that is all people will use, nobody will rely on the fact that a|b dispatches to the default implementation, they'll just never pass a|b to a single-dispatch function in the first place I should think. So it might be fine to implement it like this for now and leave only the "proper" handling for later.