There are FAA certified A&P / I&A available across Europe. For example at ACG, wich is also one of the (two) European MSCs (see also Epilogue to the purchase of a Mooney Ovation in Europe, the registration history of this aircraft was US, Finland, Germany).
I even have a FAA certified A&P / I&A at my home base EDKA.
He typically works on (and owns) several warbirds including Boeing Sterman, T6, and some T28 Trojan.
Long story short - maintaining N-reg aircraft in Europe is doable but requires some more organization and efforts than in North America..
There are several Pros and some Cons on doing so:
Pros:
US = biggest GA market around the globe, much easier for purchasing and selling
Availability of STCs and accessories (LHS for example), some STCs never make it to EASA ..
Maintenance as defined in Part 91 including basic maintenance by owner
..
Cons:
As non US citizen (or enterprise) ownership via US based trust (it's just additional cost)
For operation outside the country where your license has been issued (e.g., for me outside Germany, even if I hold an EASA license) you additionally need a FAA license or the FAA validation of your EASA license..
When an none EU registered aircraft is based inside the EU (or a certain period of time (6+ months a year or so , I'm not sure) you need a proof, that the EU import taxes/VAT have been paid in full. This is ramp checked especially in (more) southern European countries like Italy, Spain, France, .. Without a proof the authorities claim tax invasion and simply confiscate the aircraft ;-)
At least for me the Pros certainly outweigh the Cons .
Best,
Matthias