1. It's ridiculous to incorporate in the US, due to ridiculous tax policies; and
2. It's a great way to upset local tax authorities + there are probably a ton of nasty side effects (e.g. some countries have "see through" taxation that taxes certain profits arriving in foreign entities at the shareholder level, or require board meetings to be held in the jurisdiction the company is based in, etc etc)
If you do this, make sure to get advice from local counsel, or it could end up being a very expensive exercise