The alternative to invasion was a long-term blockade. Japan was already near the breaking point and there would have been millions dead due to starvation in fairly short order in that scenario.

There was probably no way to beat them without getting a lot of people killed. Leaving them alone was probably not a good option either.

I also feel a need to point out that Japan did invade the US in the Aleutians campaign, albeit a fairly insignificant and deeply out-of-the-way portion of the US. The Philippines could also be considered part of the US at the time the Japanese conquered it, although pretty loosely.