JD:
Sorry to hear about your shoulder injury and I HOPE it's nothing serious enough to be long lasting!?!
As to benefits of being able to case with either hand:
Personally, I'd never given it much thought at one time. Like, when we were all young and thus; "Would live forever and were totally invincible"!?? Yeah, right, nice notion at the time!!
But, one day, a very good fishing buddy of mine lost his right, (and casting) arm, in an industrial accident. Joe's one of those, that "has more guts than a slaughter house", so after the initial care and therapy of the arm loss was over and done with, Joe called and asked if we could go "wet a line"?!
He'd adapted himself to casting with his left hand, as gracefully and as well, as he'd ever been able to do with his right. I was not only very impressed, I was also actually envious that he could make such a transition look so easy!! So, I decided to also give it a try, to see if and how, I'd do if such a misfortune ever happened to me. And, as the type of friend Joe is, sort of an "honoring him" thing went along with it all, too.
I learned to cast, left handed, as well as I can right handed. (NEITHER hand, that I can cast with, is noteworthy, believe me!).
Well, about two months ago, I was diagnosed with "The onset of Parkinson's Disease". (Yeah, I know,even the doctors said the same things................ "Kinda "rare" in someone so darn studly, good looking and only 57 years young!). But, 'dems da' facts and OF COURSE, it just HAD to hit me, in my right side first, my dominate side for casting, and all things that I normally do, right handed!
Except, for, throwing my long rods because I have switched primarily, to my left hand for casting. without any effort. And, it so far hasn't slowed me down to much!