EDIT further information I posted below:
The US has the unique position of being able to actually enforce this due to the fact the USD is the reserve currency of the world and every country needs to stay on the good side of the US Treasury to transact in the global economy. FATCA requires all foreign financial institutions to report on any US citizen assets.
In fact, the laws are so strict, they make living abroad as an honest middle-class expat a total nightmare. I have friends who cannot find a single bank in their country that will work with them because of the reporting requirements of working with US citizens. They cannot save in foreign banks and they cannot invest either due to the US penalizing foreign Mutual fund/ETF purchases by private citizens.