Not so sure about the republicans who ran in 2016, but looking at our last republican president and I have little doubt the response would have been better and more effective. W got off the beaten track once in a while when he wanted to play his "End of Times" games, but overall I am fairly certain he would trust a roomful of doctors and researchers who offered timely advice and he likely would have had a more empathetic way of dealing with the pain of people all over the country. As a way of comparison, I think trump's handling of the coronavirus is far worse than the Bush administration's handling of Hurricane Katrina, and in some ways this crisis may have been easier to deal with since we already knew the handful of things that were going to work.
Hell, how hard would it have been for trump to just do what he did in the middle and end of March instead at the end of February and the beginning of March. Had he done so, tens of thousands would still be alive. Had we taken those measures 10 days earlier and done so everywhere (forceful leadership from their dear leader would have left hesitant governors little choice in their minds but to support trump) and if we don't get a resurgence in the fall, then this would have been handled as best as our messed up healthcare system would have allowed. And trump would only be an awful person and terrible president instead of the mass killer he is.
*eta* Actually any number of those running in 2016 would have had a better go of this than trump. Kasich, Bush, former New Jersey goverors, lots of them. These people all would have seen that doing what trump did meant thousands more would die. Doing something right means they wouldn't have. No doubt that the outcome would have been better. Either Clinton or Biden would have had as effective response as our system and society would tolerate. We would still have numbers per capita worse than a place like South Korea, but a lot of people who have died in the last 3 months would be alive and well right now.