All countries want to protect their local labor market and will not make it easy for US grads to practice without jumping through lots of hoops. Think of the "foreign medical graduates" (MDs trained in other countries) in the US: it's practically impossible for them to find a residency, even after they have passed the required tests. So they can't work as MDs because you can't practice in the US unless you have done a residency. I personally know 4 such folks, and they had to switch to other careers. Foreign-trained PTs also have to go through many hoops before they can practice in the US.
I used to work for the United Nations in several foreign countries so I have seen it first-hand. There has been a lot of discussion in Europe about recognizing intra-European degrees thanks to the European Union, but I don't know if they have reached a decision. If you want to practice in Europe, get an European degree.