I spent 3 months in Europe this year looking at boats and considering this question. I found a boat I wanted to buy in Turkey, excluding VAT. I learned that you can keep a boat, regrardless of the flag it is flying, without VAT anywhere in the EU for 18 months, then you have to check out of that country and then check back in to another country to be able to keep it again for 18 months without VAT. This works only for non-European residents and citizens. Some countries have temporary resident visas and nobody (including brokers) seems to know if they are exempt as well. I saw US flagged vessels in Spain, Greece and Turkey and the flag doesn't impact the VAT issue, just the status of the owner and the person using the boat.
Some cruisers told me "oh don't worry about it, they never check". However, I found news articles where France and Spain had impounded boats that had not paid VAT when it was determined that the owners were supposed to have paid it. That applied to British and European residents, but I also was told that enforcement is unpredictable and sometimes hard to prove that you are not a de-facto resident even when your passport proves otherwise. Several cruisers said in a blog that that they had documents from the Spanish government proving they were not residents but were threatened with heavy fines if they didn't pay an additional Spanish tax on yachts that is supposed to apply to residents.
I considered cruising in the Med for one season and then moving off to Algeria and then to the Canaries (also Schengen) before crossing the Atlantic to the Caribbean. Not being an experienced sailor I don't think I'd gain enough experience in one season to attempt that. Besides that I didn't want to buy a blue water cruiser, I wanted a lighter smaller boat that would cost less to keep in the Med.
I didn't buy a boat in the Med because as a non-European resident I can only stay in the Schengen area (Europe) for 90 days out of 180. I don't want to try to stay during the winter so that effectively means that I could sail there for only 90 days per year. I considered trying to become a resident in France or Spain so began looking for a VAT paid boat. I didn't find one and was overwhelmed by the bureaucracy involved in applying for residency. Among other things, you need to have a physical address and go back to the US to apply for a visa before you can even apply for residency. I finally gave up and am now I'm back to looking locally and in the Caribbean.
Hope this helps! Contact me directly if you want additional details.