You think things would have been different if Reagan didn’t fire Haig?
I think Reagan had enough sense that da Bush's did not in dumping the Nixon/Ford era foreign policy advisers. Reagan also had enough sense to listen to all but act wisely in most cases. His stepping away from main stream foreign policy led the way to the changes he brought about. I don't think any Nixon/Ford era people involved in foreign policy under them could have accomplished what he did.
I'd say he drove both Haig and Schultz bonkers by not staying inside the foreign policy fishbowl. I'd credit Reagan with the foreign policy successes of his day. Remember he wisely sat back and let Israel end Saddam's nuclear program. Since the end of the Reagan era all administrations have tried in vain to dictate Israels affairs. In doing so they have perhaps stood in the way to what could have been a pretty good M.E. mop up.