I think you got your idea all wrong. A specialist is someone who specializes in one art. A specialist is compared to purist. An non-specialist is someone who studies a little bit of everything. Specialist only do what they specialise in. While a General doctor may do a variety of different things in different areas. You have people who make all types of swords. An you have those who specialize in making one type Authenic Japanese Sword made for combat. The specialist only makes one type of sword. The Mixed Sword makers makes all kinds of swords. You have someone who specializes in boxing. An you have someone who practices Muay Thai,Boxing, and BJJ.
Remember the movie The five deadly Venoms.
There was sixth student who train in all five styles. But he was no match to fight one of the original Five Venoms because he didn't specialize in one their arts.
My God, I can't believe we're still talking about this. The whole idea is whether or not you can use WC and its grappling methods or if you need to go to someone who grapples. I said in another post, that pretty much every art has its methods of dealing with a grappler, BUT, if you want to improve on that area, you will need to go to a grappling based art.
If you want to crosstrain, do it. If you don't, then don't.