The US did tried to do that, it was overruled which is why the Clinton administration voted no.

The US government is not allowed to participate or facilitate a criminal prosecution that would deny a US citizen their constitutional rights there has been a Supreme Court case about this already ironically in 1998 which was also one of the triggers for voting no.

On a side note the ICC is terrible, any party can bring up a case, there is no separation of duties, no defined scope and no right of appeal.

The ICC is nothing more than virtue signaling, and should never been established in its current form the world was just too high on its own supply of late 90’s hopium at that point to care.