Luckily the EU allows N-reg aircraft to be operated here and luckily the FAA makes it very easy to convert our JAA license. This means that there are more aircraft in Europe and since you have to be an EU citizen to work in the EU it means more employment for us. If one would make it harder to fly a N-reg in the EU, a lot of them, could even be the majority of them, will not be replaced by EU registered aircraft. Having a N-reg is cheaper for the owner and allows more of them to own their own aircraft. For some there are significant tax advantages in owning an N-reg.
The current situation is good for employment, good for the owners, good for the economy.
Just to be clear I am against offering free cabottage to N-reg or for that matter all
non EU reg.
And to get back on topic, yes there are loads of N-reg, M-reg and VP-reg aircraft in the EU. All of them operated privately, some as a one man band some by management companies.