Dirty Harry,
Let's look at it this way, a Pilot from Airline A has a B 757/767 type rating on their FAA ATP certificate and is a check airman with thousands of hours as pilot in command of both at his/or her current FAA certificated part 121 carrier in the US. Now this person decides to take a Pilot position with another FAA certificated part 121 carrier in the US, do they just sign on? No they don't, they must sith through training for the company they are going to work for, aircraft ground school, flight training, check ride, etc, etc, etc... as you listed. It could take anywhere from a month, to a couple or more months to complete this process for anyone US citizen or not, regardless of if they are currently doing the same job for another carrier or not. It would be nice if we could have one worldwide system and set standards accepted by all, but we all know it just is politically possible at this time.