It could have created momentum for other major powers to join (e.g. Russia) and given the ICC broad authority to prosecute the crimes it has jurisdiction over.

That might have created a world where leaders act differently. What, for example, would have happened in if Syria and Russia had both been members?

It’s easy to be cynical about ideas like the ICC - the logic of power is hard to avoid - but the US working against it is definitely a major reason for its weakness.