Well, this question does ask for a lot of opinion and I'd like to prevent accidentally starting a heated debate over what type of martial art is better. Instead, I will show you how grappling is and isn't useful in a street fight.
How it's useful in street fight
Grappling's main strength in real life fights is that you are able to have a huge amount of control over your opponent. If you get them to the ground and you are able to secure a good lock, you probably don't have to worry about them pulling your hair or trying to bite your ear off. And if you are able to control them well, you won't even have to worry about them striking you, even small amounts. Here's an example. It's also easier to walk away from a fight after you have submitted them than after you have struck them, unless you are able to knock them out. If you punch them in the face and then try to walk away, they may very well just get back up and start attacking you again. But if you take them to the ground and break their arm or choke them unconscious, you impair their ability to fight back while you run away.
How it's not useful in a street fight
Well, the first thing, is that if you are being attacked by multiple people, most grappling arts are unlikely to be effective. Secondly, if you you miss your opportunity to gain control of your opponent and take them to the ground and they have started raining strikes upon you, it can be very hard to start applying grappling techniques right then. That's why if you intend to use grappling, you should manage your distance from your opponent: Always either be too far away for them to touch you, or close enough that their strikes become weak and you are able to gain grips and take them to the ground.
Whether others agree with it for the most part or not, this is a fairly opinionated question, so it is only reasonable that I share my opinion, built on experience, or course.
My opinion is that if you want to learn self defense, grappling is an essential skill to learn. It is extremely effective against one opponent and gives you the ability to control their entire body while simultaneously attacking them. However, I also believe that the best thing for self defense is being well-rounded in multiple styles. Punching, kicking, grappling, throwing, submitting, are all skills that one way or another will be useful for self defense in their own ways. Each has strengths and weaknesses.
If you are looking to learn martial arts for self defense, a some popular choices are
- Muay Thai and BJJ (Gracie schools will be most likely to teach self defense-oriented curriculum, instead of competition-oriented)
- BJJ and Taekwando
- Mixed styles of Kung Fu like Wing Chun and Tai Chi
- Krav Maga and BJJ or Wrestling (any kind)
I do BJJ and Krav Maga because BJJ gives you the knowledge necessary to win fights on the ground, while KM teaches you all-around self defense from standing, including against multiple opponents. I'm not by any means saying that this is the best combo, but I do find it extremely effective. I have no doubt that the other combos are extremely effective as well.