There are clearly a multitude of different reasons why some "Euroland" residents have found themselves flying foreign registered aircraft that are based in Europe, its not always as simple as some would like to believe.
I was married and living outside the EU. I had a UK PPL and was offered a very attractive entry level flying job on condition I got myself a FAA CPL/IR with a minimum of 500 hours. I jumped at the chance and found myself in the USA, CPL/IR, CFII and instructing to gain the hours required. On returning home that country decided not to grant me permission to work as a pilot and then my personal situation changed and I returned to the UK. I then embarked on the enormously expensive conversion to the UK CPL which I eventualy gained with the required sign off for the IR check ride. Weather precluded my test and whilst waiting was offerd a job flying N reg aircraft resulting in a command on a Citation. This led on to more and more interesting positions and the UK CPL gathered dust and was largely forgotten. I am now no "spring chicken" and finding it more and more difficult to find work, do I want to spend a fortune at my stage to obtain the EASA ATPL, of course not.
My point is that for whatever reason an aircraft is LEGALY on a non EU registration, it still needs a suitably qualified pilot to fly it. If the owner has chosen to have his aircraft LEGALY on that registration, he should have that freedom of choice. Shopping around for the most cost effective way of doing ones business is an accepted practice in any industry.
This entire issue is only about training, i.e. who would choose to train in Europe when the cost is so much less in the USA? Europe's only answer is to not accept the FAA licence to force the issue and protect the European flight training organisations at the expense of the individuals who need training. They wish to curb our freedom of choice in the name of protectionism with no consideration of safety whatsoever. I only intended to address the case for the pilot here, not the case for the decision to have the aircraft on a foreign reg in the first place, that is another discussion that also has a multitude of different reasons.