I doubted that "many" expats give up their US citizenship so I tried to find some numbers. Found some secondary sources like: https://www.forbes.com/sites/robertwood/2018/05/14/fewer-ame...

which states that, worldwide, just over 5,000 Americans renounced citizenship in 2017. There are also about 9 million Americans living abroad and ~1 million living in Europe. So, no, I don't think that even if all 5,000 were in Europe that 0.5% renounced their citizenship would count as "many".