yes, for sure this is a logical extension of republican thought ( so would have a wildly libertarian government been ) – but it is not simply a failure.
the current administration has actively underminded the response in a way that no other administration republican or democratic would.
this is not some economic crisis in which people believe that more capitalism will solve the problem, and can rollout economic experts to concur.
this is a healthcare crisis with no experts at all saying that what trump is doing is good.
does this further undermine trust in government in general? sure, definitely. probably we will have to see what happens if/when biden gets elected.
but again the failure here isn’t in the people. it’s not our lack of trust that’s killing us.
it’s that he’s actively harmful. we don’t, in fact, want people to trust in this government because that’d get even more people killed.
if this were any other administration in the modern era, they might not have taken it seriously initially, they might have made some mistakes, but i cannot imagine any administration which would have shown this level of malice.
at this point you can pretty much guarantee that the opposite of what trump recommends is best. even bush jr, heck of a job brownie, and all his warmongering buddies weren’t this counterfactual.