Lets be clear regarding protectionism and pilot jobs...the licensing laws in JAA land are a form of protectionism.
It is a given that you need the right to work in a country (citizenship, greecard/visa) before an airline will offer you employment.
However, it is MUCH easier for a European with the right to live in the USA to convert licenses and gain employment than it is for a Yank to convert and work in Europe. It would cost a European about $5000 (maybe) and a month or two to get convert a JAA ATP for a FAA one. It would cost an American ATP holder about $20,000 and at least a year to go JAA.
Flying in the USA for an airline for just over a year, I have flown with Captains and known FO's from from Sweden, Finland, England, Jamaica, Argentina, Japan, S Korea and Columbia. Many moved to the US for a better career path (how times change!) How many European crews have non-Europeans there? And how many are in Europe for family reasons and HAD to convert to get a job (as opposed to going to JAA land to get a job and then getting married for example)