If they're planning to do something that might get them indicted for crimes against humanity, then they are not reasonable candidates.
Allowing external courts to judge presidents is a bad idea. It is a slippery slope even for cases that seem obvious. My 2c.
It does not have a history of "slapping any label on any suitably vilified candidate".
Put another way: The US has a history of deciding it is allowed to start actual wars to overthrow the kind of people committing the kind of crimes that gets you targeted by the ICJ.
The US just wants its own people to not be subjected to what it has a long history of imposing on others.
I don’t know what the solution is. But an essentially advisory body like the ICC probably isn’t it if the goal is checking the U.S. and its allies, or China and its allies. (Maybe it’s useful for checking Western Europe? Idk.)