

Ironically enough, you actually have to pay the US Government to renounce your citizenship. The base fee is $2,350, but the application process is so lengthy and complex the total cost can run up into the $20k range. Oh, and you’re still obligated to pay taxes and subject to the draft.
For taxes: initially it was because business owners were renouncing their citizenship as a way to avoid income and capital gains taxes, as well as estate taxes. Once that was done though then the feds realized they could squeeze everyone.
For the draft: during the Vietnam War people would flee to other countries (usually Canada) and renounce their US citizenship, even if they didn’t obtain citizenship elsewhere. Becoming a stateless person was (correctly) seen as less of a death sentence than being sent to Vietnam.