I don't like mangling words.
"Universe" means everything, so it can't be a subset of multiverse.
It's not science. It's vocabulary.
It does not mean that, true, and thus cannot be valid as "universe" is already defined in the language to include everything everywhere always.
If it did mean that, then it might be worth considering.
Yes.
If the meaning of something is "everything everywhere always," it has no replacement as a concept.
That's what "universe" was intended to mean.
So a new term was coined to describe a concept that didn't exist back when the old term was coined.
The word "multiverse" is just a more convenient way to express the idea of multiple realms of reality which coexist but cannot be observed by the beings residing in each.
It's just a shorthand term.
Nothing to get hung up on.