Why on earth would the US export when it's supply-constrained itself? Of course, the US can and will export once it has sufficient supply. But countries exist in large part to look after the self-interest of their own population. It would rightly be a complete political non-starter for the US to start shipping vaccines elsewhere while it still needed more doses domestically.
Don't you think Europe is supply-constrained? What about India/Russia/China?
If these countries didn't export, Israel wouldn't have any vaccine, Australia wouldn't have any vaccine, Canada wouldn't have any vaccine, New Zealand wouldn't have any vaccine. And let's not even talk about the rest of the world.
But yeah, it's inconvenient. I get it. Greed is good! Let them starve.