I think, when it comes to self defense, it's a really good idea *not* to be specialized in anything, unless that speciality is, itself, a diverse and wholistic approach to self defense.
In competition, people specialize to the a very specific ruleset and environment of the ring.
In many TMA's, people specialize equally, with the context of fighting other practitioners of the same, or similar art(s).
But in the real world, you have to unspecialize. You have to know something about dealing with committed, untrained opponents, as well as opponents who may have some experience. You have to know how to deal with not just grappling and striking, but potential weapons. You have to know how to deal with multiple attackers. You have to be prepared to deal with people much larger than yourself. You have to know how not to injure yourself by breaking your hand, slamming your knees into the concrete, etc. etc. And you have to not just be concerned with fighting, or winning the fight, but with extracting yourself from the situation, with legal concerns and reasonable use of force, and with avoidance and de-escalation.
So in short: don't specialize. You need to have a keen understanding, and ability to operate under immense stress against a very wide range of threats, and to stay tactically aware such that you are creating every opportunity to avoid, end, or escape from the situation and protect yourself both physically and legally as much as you can.
Of course, if you have a specific role, such as Security / Police / Bouncing, etc., there is understandably more argument to be made for specializing, as you have in those cases a more clearly defined role and expectations beyond just protecting yourself or people around you.