The more I train and the more diverse people I come across in MA (diverse meaning reasons and goals for training), the more I'm convinced that fighting and SD are a state of mind. There's a mindset involved that most often determines that person's success in defending themself. I've met a lot of excellent dojo fighters who I wouldn't want backing me up when stuff hits the fan. I've met a lot of people with zero training that I'd want at my side in a heartbeat.
The dojo is a controlled environment, even though people may be training at full force/resistance. Competition is a controlled environment, albeit less predictable in what you'll encounter. Same for the cage.
Elite fighters are elite for many reasons; they're mentally tough, physically tough, and are athletically gifted. The combination of all those things makes them elite. No matter how physically tough and athletically gifted you are, if you're not mentally tough, you'll only get so far.
Full contact/fully resisted training can help with the mental toughness. It teaches people they're not made out of glass and can actually keep going even though they've been hit. They realize a punch to the stomach won't kill them. It helps them to keep moving forward despite getting hit. It teaches them to not fall down and cry in a fetal position. It also teaches them to hit with intent and hit hard. Training like that will help with the mental toughness. It doesn't matter if it's TKD, karate, kung fu, judo, jujitsu, nor anything else.
It takes a certain mindset to fight. Not everyone has it. And not everyone who does have it wants to get into the ring nor the cage to prove it. I've got better things to do with my time than train at the intensity and the duration that aspiring fighters do. I know that if I had no other choice, I could throw a pretty good beating on a lot of people. I also know there's plenty of people out there who'd easily do that same to me. And I'm smart enough to know you can't judge how much of a challenge someone will present by just looking at them.
Do not know karate works? I know I work. Would I be more or less effective if I studied any other art/style? Maybe a little bit either way, but not much. Would I be as effective if I sat around every day doing absolutely nothing? Absolutely not.
Also keep in mind that competitive fighters have time to prepare for who they're fighting, and know who, when and where. A guy walking down the street minding his own business doesn't have any of those luxuries. One minute he's having a great time chatting up some young lady at the bar and before he realizes what's going on, some tough guy is grabbing him and trying to choke him out or punch his face in.