NLP is a domain specific problem. Of course it shouldn't be under computer science. Pure computer scientists are much less useful than linguists for these things. That's like arguing that building physics simulations is under the realm of computer science. You'd want your team to be mostly linguists, some which specialize in computational linguistics. A vanilla computer scientist, to be frank, is almost useless, especially at the PhD level.

I think it matters because it determines what kind of people you would hire to do the R&D.