You are asking for an essay on aviation regulation, politics, and this could be pages of stuff - even if one keeps out of contentious issues.
I don't know how much you know about flying but, in a nutshell, to get worldwide IFR privileges you generally need the country of aircraft registration to match the country which issued the Instrument Rating (IR). Why? Don't even ask.
Here in Europe, a pilot can get the Euro (JAA) IR, or he can go abroad and get some other IR.
To fly IFR in a G-reg plane, you need the JAA IR. This involves a very long ground school and other hassle. It's designed for airline pilots. There is no special Europe-wide provision/concession for private pilots.
An IR which is much more accessible for a private owner-pilot is the American (FAA) one. But this needs a US-reg (N-reg) plane.
Hence you see N-reg planes based in the UK, and other countries in Europe have similar issues.
There are other reasons for N-reg e.g. many planes have not been certified in Europe, so they have to be on the N register to fly at all.
Politically, this is provocative to the national aviation regulators, and they are trying to stop it. But it's difficult, because international aviation treaties permit unrestricted visitation. So only long term parking can ever be controlled.
There is a lot of sneering at the N-reg scene, by some Euro IR holders who regard themselves are superior, which is another thing.... UK flying schools also don't like it because they can't do the training... well actually they can do nearly all of it but it's a lot cheaper in the USA. The whole picture gets very muddy because of various ways of doing it.