To white belts, I teach Gracie Combatives, which is strictly self-defense. And of course, I offer Master Cycle to non-beginners, which is self-defense and sport. While I’m on the self-defense side, I stopped making a big deal about it a long time ago.
The truth is, most of us will never get in a fight. And we can become punch-safe in around 100 hours of training (about a year of twice a week classes).
The real argument is which to train first, and self-defense should be first, because most people quit within a couple of years. And if that person gets in a fight—very unlikely, but still possible—they’ll rely on whatever little training they had, and we’d hope it was self-defense.
After two or three of years of training, no matter if it was at a self-defense or sport-focused school, the student should by then be OK at both, so the debate can end. Just train both and never quit.