I keep all invested assets in the US, which has the world's most transparent, efficient, and inexpensive markets. Investing as an American in European mutual funds, ETFs, etc. can be very tricky with respect to taxes (both US and the European country you live in). So, be very cautious about this.
I use Schwab as a brokerage and bank in the US but also have some Vanguard funds (TIRAs and Roths). I maintain a US address for this purpose. I transfer funds to my local bank in Switzerland from Schwab in the US using Wise (formerly called TransferWise). The rates are low and the transfers are very fast and have been getting faster over the years. Never any problems.
It works as follows: I transfer funds quarterly. As income accumulates in the Schwab account I initiate (online) a Wise transfer from their US domestic bank to my Swiss bank at a guaranteed mid-market actual FX rate plus a small fee. This results in overall costs that are significantly lower than bank-bank international wire transfers. Wise then waits for the exact amount I am transferring to show up in their US account (along with information identifying me as the transferee).
I then do a domestic transfer to that bank from my Schwab account. Schwab charges $15 dollars/transfer but the first three each quarter are free. Hence, I try to do only three per 90 days and cherry pick the best FX rate days. I find that the domestic wire transfer (Schwab to Wise bank) is measured in minutes, start to finish. Then Wise picks up the funds from its account and I receive my funds in my account within x hours (Wise estimates the time of receipt at my bank and is usually right).
The reason Wise is cheaper is because it doesn't actually transfer your funds, but instead pays them out to you in your own country and in its currency from a bank account it maintains in your country. So, for them always a domestic transfer. Wise keeps me updated via email of their steps in the transfer process. Note: I employ email/text alerts from FX sources so that I can be assured of a good rate that might pop up on any given day. It makes a difference.
FATCA is indeed a huge problem for Americans in Europe and around the rest of the world. Most banks just won't allow American accounts. I was asked to cancel my account within 24 hours of notice more than a decade ago. In Switzerland the bank of the Postal Service must, by charter, allow any customer to have an account, so they are the default. But UBS has a set up for Americans--they wall off this group in a way that avoids much of the FATCA reporting from the rest of the bank.
As US citizens my wife and I have to fill in a joint report (online) once/year detailing all of our non-US accounts, via the FBAR report. We are below the thresholds for detailed FATCA reporting.
-BB