As far as street fighting is concerned all you really need is good boxing and wrestling skills. Stay on your feet, don't get taken down, and if you do get taken down have the ability to get right back up.
I started martial arts because my friend's dad was an instructor and two because my friends got into a lot of fights. And street fights are totally different, confined spaces, number of opponents, materials around you... You also don't have hand wraps, broken hand if not careful... However, it doesn't mean MMA, boxing, or BJJ can't help you or translate into street fighting self defense. It's sometimes not practical to use a certain style in a certain situation that's all. Also consider that MMA is probably the greatest for self defense since there are rules and just like MMA we have laws in the real world that determine whether you defended yourself and/or restrained the person or assaulted them even if they attacked you first. Legally it's better for you to KO someone then to armbar someone and snap an arm. You'd have a 50/50 chance of getting assault charges with a KO and almost definite charge with an arm snap even if you were hit first.
I've trained, Judo, BJJ, scholastic wrestling, boxing, Muay Thai, and JKD. I loved BJJ until I was taught boxing. Boxing is just out of this world. Also learning how to disarm weapons along with good running shoes is also a good idea. Sometimes it's just better to run fast as hell. I remember doing JKD and the ground work, they use to tell us to gouge the eyes, pick up weapons, and do anything possible to stop your opponent, lol. Sounded good then...