For the same reason as any other treaty - the corresponding benefits.

> If the US wishes to discipline its service members, they still can and do.

That's not what the ICC is for. The ICC is for when a country won't do so when they should be.

> Under no circumstances should any country allow a foreign entity to decide what its military can and cannot do.

The US has a very long history of telling other foreign entities what they can and cannot do.

Its not “service members” that are the usual defendants at the ICC.

If US soldiers are (once again) committing war crimes, will the US do anything? What’s the recourse for the victims of those crimes? Should there not be one?

The war crimes (and some others) that are subject to the jurisdiction of the ICC are already crimes recognized explicitly in the treaties establishing them as crimes matters of universal jurisdiction. Yeah, its difficult to get your hands on them to exercise that jurisdiction, but... that hasn’t really been a problem the ICC has solved with regard to significant powers when their personnel are subject to its jurisdiction, either.