There is the direct financial cost of paying US taxes when living abroad, but it is also a significant cost in time and energy to file taxes for 2 countries. It can get pretty complex, so many need to hire a tax service to handle it properly.
Then there are the additional reporting requirements for any banks that you have accounts with, so some banks will not allow you to have an account with them because you are a US citizen.
The point is that there are some real downsides to maintaining US citizenship when living overseas.
There are many upsides of course, like being able to return to the US at any time and live and work there. If there were an emergency situation, I could probably count on the US embassy to help me evacuate if necessary.
Overall, it's a cost/benefit evaluation. If you have citizenship in another advantageous country (or country in a powerful union like the EU) and significant resources, I can see why it would be tempting for some to drop the US citizenship.
[1] https://www.irs.gov/individuals/international-taxpayers/figu...