As for people discarding evidence, proving "Brand A of universal healthcare is Bad" doesn't say anything about brands B-Z

There are obviously possible counter arguments that demonstrate that a vast majority set of possible implementations are bad. The possible implementations of any intention are likely to share a number of crucial parts. There are only so many ways to get to a place. E.g. If I think more health care harms health outcomes as much as it helps then I am going to oppose any implementation that involves subsidizing health care. And of course I could have as many such arguments as I like. If I have fifty arguments that, combined, show that all the possibly implementations of universal health care are harmful than I have good reason to oppose the intention of implementing universal health care. And I don't have to exhaust all the possibilities: I just have to have never heard of an implementation plan that I didn't think would be bad.

Not to mention: "universal health care" doesn't actually mean "everyone gets the health care they need" it means something like, "everyone gets the health care they need through some new government mechanism". "Increase per capita GDP and lower health care costs though economic growth until everyone can afford what they need" might the best way to get everyone covered, but it would never be called "a plan for universal health care".

Obviously, "that rout to Jamaica is tricky, you can't go South there" is not an objection to the basic idea of going to Jamaica. But "Jamaica is a terrible place" is. So is "40% of people who try to get to Jamaica die en route". So is "we don't have that kind of money". So is "Jamaica will turn you away at the border and it is too dangerous to sneak in". "I don't like nice weather" is also a basic objection. But it's an uncommon one and mere opposition to going to Jamaica is a really bad indicator that someone doesn't like sunny days.

I'm not saying you need to determine every detail of the implementation of a policy before counting oneself in favor of something. But policy goals are not determined in the abstract. There are important, basic facts about economics, human nature, and government that yield heuristics about what policy goals are beneficial and which are harmful.