For some reason, this surprises me. I have seen countless calls for Apple to be more open in general (do not want), but your suggestion would only open it up to other browsers. I'm intrigued and torn: I feel like Mozilla might have something to contribute there, but I feel like Chrome would follow on by wanting their own App Store.
I think I agree that Mozilla Firefox using its own engine and extensions would be a valuable app. I'm not convinced I would want to let anybody else in.