Since we're talking ethics, do you also think universal healthcare should be provided by wealthy nations to all the world? Otherwise we are just picking and choosing based on where someone happens to be born, aren't we?
At the core of it what you're basically arguing is that nations are unethical because what citizenship someone holds influences things like their access to health care, and the solution to that would probably look a lot like the EU but completely borderless world-wide (with no immigrations or customs departments?)
I think you know how people would react to that. It's a pointless 'gotcha' question
As for national borders being unethical by nature, if that logically follows then why not?
I certainly don't consider ethics a source of "gotcha" questions, but of real conundrums.
Not really. A huge amount of charity money supposedly going to the poor in other countries is actually used to bribe officials in those countries to allow the aid to be delivered. Any attempt to give healthcare to people in those countries would also be seen as foreign interference, and suffer the same problems.
As regards providing free healthcare to anyone regardless of country, that seems next to impossible without providing the infrastructure necessary within the country they live, which would indeed be very difficult to work out. It seems like a good goal to work towards - everyone regardless of nation having access to reasonable quality healthcare.