The composition copyright is listed in Brawl as belonging to Akira Miyagawa (the show's composer). I can't imagine what exactly went on but my guess is that as it was cut in Smash 4 they didn't want to jump through the same hoops to nab it again (granted, that game had far more going on in it than MK8, but still).
Regardless, I want to be proven wrong and now absolutely need this idea to become reality lol