Renouncing one citizenship without first acquiring another is a great way to destroy your own freedom of movement and generally undermine your own quality of life. Stateless persons are usually treated according to the amount of wealth they possess. As someone not particularly rich (by Western standards) getting free of the US requires chaining yourself to a less objectionable regime. As might be expected, the countries that people want to live in have stricter immigration requirements.

The "just leave" escape valve is thus not very effective whenever the pressure builds too quickly. Besides that, the smartest and wealthiest people leave first. Anyone left behind is less able and possibly less willing to defuse the crisis.

For most people, they have significant investment in their local community, with financial, social, and reputation capital built up over many years. Abandoning that represents a huge loss, and would require a proportionally large threat to even be worth considering.

I don't expect emigration to change anything, unless some other country miraculously changes its policy to out-freedom the US, and thereby suck all of its brains out.