4K doesn't have to advance game design. If high definition wasn't a thing, we'd still be playing on standard definition and we would be none the wiser. That's beside the point. Nintendo shouldn't be artificially holding back for arbitrary reasons which we've seen it do so many times in the past. If 4K can be supported reasonably and responsibly, Nintendo shouldn't deny their partners (or consumers) the option. For example, say Square-Enix wants to develop a 4K Final Fantasy, it benefits Nintendo to be able to offer that possibility. Still, if that means NX launches at $500 or something, the disadvantages outweighs the benefits. It would be fantastic to get killer apps that offer something extra PS4 and One can't, especially something like graphics that the general public immediately gravitates toward. Nintendo just shouldn't price itself out of competition.
Full disclosure: I don't have a 4K anything. I bought a very nice 55" 1080p TV last year which I intend to use for the next five years at least. That said, 4K support isn't something I'd immediately benefit from. However, from a business standpoint, Nintendo really can't afford to keep making short-sighted decisions. Sometimes, it has gotten away with it (e.g no right circle pad) and sometimes it doesn't (e.g. friend codes and online support in general).