BJJ first and foremost is self-defense. Yes there is the sport element. And yes there is combate jiu jitsu which allows striking in the sport, and it's not mma. Boxing may not allow takedowns, but there is some clinch work and some basic limited grappling. Muay Thai is very much grappling based in the clinch. Jeet Kune Do has plenty of grappling despite being a striking art. Okinawan Karate is argued that it's origins are actually grappling and not striking.
Wrestling is the only grappling that I know of where striking is not a factor, and even then, I've been hit pretty hard by a wrestler where it may as well been a closed fist.