Let's not fool ourselves. They are mainly prize fighters, despite the "martial arts" name of the sport.
Combat sports are an ancient discipline existing across distinct and varied human cultures and every mature form acknowledges this constraint by having a third party to referee the match.
I'm not sure your distinction has any material significance here. As others have pointed out, the referee is there to stop the fight and the fighters are trained to continue until the such a time.
Fighters often do stop, an example from just last week is Bahamondes vs Giagos (although this is probably not a good example of avoiding concussion).
https://youtu.be/X2Z1En-eAgk?si=8lBY27afFMfv_Z90
But there's many, many examples of fighters stopping when they know their opponent is finished, and IMO only very few examples of fighters egregiously not stopping.