It is probably by a mixture of carrot and stick that TSMC has been persuaded to say "yes" to the United States' proposal. The carrot will be the subsidies that are de rigueur for the setting down of any wafer fab. The stick will be the threat that if TSMC does not come to the US, Apple might start buying a larger proportion of its silicon from another source. About 23 percent of TSMC's revenue came from Apple in 2019, according to reports. The only company close to competing with TSMC in leading-edge digital silicon is South Korea's Samsung.
Obviously, the US could easily print up an additional $4 billion or $5 billion if that's what it takes to persuade a blushing TSMC to come and stand alongside it.
But it is also notable that TSMC has opted to set down what is now a relatively small wafer fab that is not quite at the leading edge. The Arizona fab is denoted as a 5nm unit that will ultimately have a manufacturing capacity of 20,000 wafer starts per month. That feels like almost a minimal viable size for a production fab at 5nm.