The ICC...not sure how thats counterfactual. The current state of affairs is that the ICC has universal jurisdiction, which means that theoretically our soldiers can be brought under it--a system where we help nominate judges and provide other logistical resources seems to suggest that we would have more control over this. Also, we could help define the norms of what genocide is and not to ensure the system wasn't abused. Second, norming non-intervention is good for our hegemony. Third, if genocide escalates--particularly near oil, SLOCs, or scare resources, thats a threat to our hegemony. Fourth, the arguments I previously advanced for multilateralism enhancing hegemony. For instance, multilateralism solves balancing (like people saving shove off in the WTO), solves burden sharing which is critical in a world of scarce resources post-iraq, allows us to have bases for quick deployment, equals information sharing and global collaboration, and the UN/Nato empirical example post WWII. Also, multilateralism solves the problems associated with overstreach and the pre-emptive doctrine--ie norming the intervention is good & legitimate.

You claim that we would heighten our hegemony with accession to the ICC, but this is a counterfactual in need of more exploration. (I will also set aside the realist objection to the ICC on the grounds that the forerunner to the ICJ has (a) been horribly slow and ineffective and (b) inevitably applies "victor's justice.") Hegemons are, after all, fairly jealous of their power, and only surrender some sovereignty (as in the WTO case) when the payoffs can justify it. Furthermore, your invocation of the CTBT doesn't fit with the ICC example, as the US is a functioning member yet her membership in that organization has not prevented defections or cheating, especially as the barriers to entering the nuclear club have gone down. (I presume that you intended to argue in the ICC example that the presence of the hegemon as a member would add pressure to malcontents to follow the organization's rules.)

Here's the sticky wicket part. I think that NATO and multilateralism allows for an archimedian point for US hegemony, or as Greenspan might refer to it a "Goldilocks" hegemony. NATO certainly allows us some military and economic advantage in Europe, but not to the extent that it would provoke hostility. Multilateralism, like the ICC and the CTBT allows us to maintain our position as police power without becoming the vigilante who uses either military intervention in the case of the ICC or mini-nukes (or at least tests for mini-nukes) in the case of the CTBT. Does that answer your question?

[W]ith incredibly rare exceptions, the United States or the EU or China will adhere to adverse rulings made by the WTO or other international tribunals so as to ensure that others will do the same.

However, this leaves out those myriad cases (for example, IPR in China) where a WTO member violates the rules yet nobody has the desire to actually press the issue because the WTO bureaucracy moves slow or because it invites counter-filings by the targeted parties...

So it's one thing to say that people listen to the authorities after a decision has been made, and the historical record agrees with that, but in the WTO (as in the UN), there's strong disincentive to declare that rule-breaking has actually occurred, since it "makes too much work" (for lack of a better term) for all involved. A case in point: according to the UN, will there ever be a "genocide" in Darfur?

Second, its a question of is vs. ought. Even if it doesn't constrain us, it doesn't mean that we shouldn't follow it or that other countries shouldn't follow it or that its not useful. International law creates a norm, which even if its not perfect, creates a baseline to talk, evaluate, and create accountability for countries in the international sphere.

Third, international law matters. Our engagement of multilateral institutions is critical for coalitions of the willing to solve issues of genocide, proliferation, poverty, and every other conceivable international problem including terrorism. Professor John Ikenberry at Georgetown University makes a very convincing case for this line of thinking in Foreign Affairs in the fall of 2002 (he's had some follow up articles elsewhere as well).

Shake and Becker in Policy Review make additional arguments that are devastating to unilateralists who would keep us out of international institutions like international law. Its pretty undeniable that unilateralism leads to overstretch. For instance this administration has been radically hemmed in dealing with important issues of national security in Iran, Sudan, and Asia (I don't think even Levey and Brown take this into consideration in their manifesto). In fact, it was overstretch that led to the decline of the Roman empire (thanks Christopher Layne). Further, the formation of NATO has been critical to the economic prosperity, US leadership, and relative stability post WWII. A world without Nato would have been far worse and its hard to calculate how its serve to solidify the economic relationship that maintains about 1/3 of world trade. Thats a pretty convincing record of a nearly a hemisphere of prosperity that probably would not have existed otherwise.