>2. All allies lose confidence in the U.S. nuclear umbrella, and they create their own nuke programs. 3. Japan and S. Korea produce nukes nearly overnight. Lots of other countries follow. We now have a much worse nuclear arms race.

This is a much better solution, not worse, because empirically the only thing that stops countries being invaded is having nukes, so the more countries with nukes, the fewer invasions there'll be.