As a US citizen you have right to work in most of those countries.

Nope. Absolutely none of those appear to allow working with just a US passport.

Without that right, it would be a different story

… Because I think it is.

But, to be fair, I only did a little searching. If you have a reference - like a page from the gov of Denmark saying “Yanks are cool: come in and get to work” - I’d love to be proved wrong. My nephew needs to see the world, and working is how it’s done.