I'll preface it with the only part of the US argument against the ICC that is somewhat principled and reasonable: there is some concern that it'd be used for political prosecution of US service members or decision makers outside of constitutional guarantees like a jury trial
I don't think it actually would happen if it joined but since it's the US I can also imagine someone being pushed to (or doing it for some personal fame) to bend the procedural rules to at least launch an investigation that wouldn't generally be launched if the facts were the same in another western country.
That being said, their accusations towards the ICC as it has operated so far (as opposed to why they don't join) are mostly pretextual and right now they're mostly motivated by their alliance with Israel which is being investigated over Gaza
I don't think it actually would happen if it joined but since it's the US I can also imagine someone being pushed to (or doing it for some personal fame) to bend the procedural rules to at least launch an investigation that wouldn't generally be launched if the facts were the same in another western country.
That being said, their accusations towards the ICC as it has operated so far (as opposed to why they don't join) are mostly pretextual and right now they're mostly motivated by their alliance with Israel which is being investigated over Gaza