Submission is doable, and useful if you are well trained. And BJJ is not the best art for that, believe it or not. In Ju-Jitsu that's all we trained was for submitting in class (couldn't be breaking each others arms).
But as for the street. I don't recomend it. If the attacker is someone you know, that's a different situation than an unknown person in the street. Some drunk friend is not going to take as much technique and effort to control than a skitzer freak boy that muggs you in the street for crack money. Or a rapist that wants to violate you and then kill you so you don't tell. Or some stupid gang crap, where they don't care about human life and kill just because they can. Think. Use what the situation calls for.
I'm not subduing some rapist, gang banger, drugged out punk, or mouthy street thug. I don't look for trouble, and these types of street confrontations are no game or sport. It's kill or be killed. Don't even begin to kid yourself that because your a martial artist that you should take it easy on these types of people in the street.
Whether it's self defense or not, are you going to hang around after being attacked, waste the guy, and then wait for the cops to give a statement to?! Think. No way I am! Screw that, if the person is trying to kill you and you have to kill or maim in self defense why put yourself in that situation? Especially for some unknown person who picked you as a victum?
Now, if the person knows you, it's a different situation. A friend, accquaintace, whatever knows your name, where you work/live, then you have more to deal with. I don't know about men. But women are killed, and raped 90% of the time by someone they know. So what you as a man would do with that situation is different than what I would do.
I've talked to a lawyer on this topic. And he informed me that as soon as someone even flinches at you in a hostile manner, verbally threatens you, or acts like their going to perform violence to you that is considered assault. Done. They've assaulted you and you defended yourself.
If you think about this crap while in the street you'll get yourself killed. Live to fight another day, even if that other day is a day in court.
These are all specificly different situations that you must have some idea of what you need to do to survive. What a man needs to do is different than a woman. If you know the person is a friend or co-worker, whatever then you are limited to what you can do morally and legally, if it's some crazy crackhead your options are more abundant.
My motto:
Live first, go to court later.