While I agree with the logic you present, you don't really disprove the US-first mentality OP is mentioning. Which is pretty fucked up approach for anybody outside of US (like it or not, its 95% of the mankind). Where would this finish? Should we treat only US persons (a number which is rising exponentially just like anywhere else), and only after this is fully covered should we care about the rest?
You might have not intended to make it look that way, but after what Trump pulled (yet again) with trying to bribe German company to produce vaccine ONLY for Americans (German government confirms that, so I have 0 doubt its true), he pissed most of the world pretty badly with this selfish approach.
I get it, he has absolutely 0 morals and would sell his mother for profit, but this is lower than low.
This is a global problem, and we need to treat it as such. US specific ones will simply get little support from elsewhere. Just like nobody would expect too much US participation in solving mainly Lithuania issues.