Maybe I'm missing your point, but what stops Americans from having a say in its laws and procedures? If the US signed on, Americans would have the same voice as everyone else, no? Though I guess its voice would actually still be louder, because the ICC draws its power from the member countries.
Regarding the accountability - yes, it's not solely accountable to the American people. That's the core idea behind an international court: it is not beholden to any single country.
> Many of its member states are themselves semi-democratic or totally autocratic. People such as Afghani women, for example, have no rights at home and by extension no say on the procedures of the ICC, but they can be judged by it, because their dictators are signatories and do have a say.
While I get the idea, I'm not convinced that the absence of an ICC-like institution would in any way help disenfranchised people with gaining these rights. As the last few years have shown, the US - left to its own devices - will gleefully support an ongoing genocide.