@Hanzou There is spillover from sport to self-defense. But a lot of sport folk just assume they can use their sport training in any situation. That they'll just figure out how to deal with any differences in the actual engagement.
For example, I've had plenty of wrestlers or BJJ guys tell me that they would just use their wrestling or BJJ for knife defense. They wouldn't train it, but if someone attacked them with a knife that's what they'd do. Clinching up is great for stopping power punches from landing, but might make it easier for them to stab you repeatedly.
Same thing with eye gouges. A lot of MMA folk seem to think the only way of attacking someone's eyes is to throw a claw hand like a punch. It's not. I can attack your eyes any time my hands are near your head, because it doesn't require much force.
They also don't address things like awareness, deescalation, when to fight, what to do after the fight. Because in a sport match, there is no deescalation. You know who your opponent is. And after the fight, it's over.
These things can be covered by a sport art. But lots of sport artists tend to quickly dismiss any situation outside of their sport (or outside of MMA) as being impossible to train for, unlikely to happen, or something they can handle easily without having trained for it.