ICAO (International Civil Aviation Organization), does a pretty good job keeping things standard across international boarders. The FAA maintains a list of 3rd world airlines that are not allowed to fly in the US because of safety concerns. Most developed countries have standards as good or better than US so registering A/C overseas won't really help anything. A lot of US airlines ship heavy maintenance offshore because of cheaper labor, that's a concern.

On the other hand, and quite unfortunately, I think foreign carriers are interested in open skies/larger ownership in domestic carriers because we represent the low cost/cheap labor in the civilized world. Which is good for our jobs, bad for our bank accounts.