Last I checked non-Singapore citizens and Permanent Residents need an Employment Pass (EP) to work as a skilled worker in Singapore and such a pass must be applied for by the employer. So under that scenario you need a visa and sponsorship by an employer. There is a new system called PEP which does not require sponsorship by the employer, but has additional requirements in terms of base salary and restrictions on employment, but again it still counts as requiring a visa.
So having "just an American passport" does not allow you work in a country like Singapore without applying for a visa. While the Singapore system might be more flexible than other such as the US, it certainly is not "free movement of labor".
So having "just an American passport" does not allow you work in a country like Singapore without applying for a visa. While the Singapore system might be more flexible than other such as the US, it certainly is not "free movement of labor".