Essentially if you want an official full time work, you have to have a right to work in the U.S. It doesn't matter if you are remote.
If you want to be a contractor there is no such requirement and you may work for a U.S. customer from anywhere and don't need a right to work in U.S.
And yes, almost everything in software is 'U.S. phenomenon only'. I for example, just skip European customers because they are too difficult to work with and pay too little, they don't worth the worry, and their projects are hopeless anyway.
If you want to be a contractor there is no such requirement and you may work for a U.S. customer from anywhere and don't need a right to work in U.S.
And yes, almost everything in software is 'U.S. phenomenon only'. I for example, just skip European customers because they are too difficult to work with and pay too little, they don't worth the worry, and their projects are hopeless anyway.