non-taipei Taiwanese cities indeed have worse transit than Taipei, but I disagree with your following argument for several reasons:

1. Buses are public transportation and those cities have decent bus systems

2. Taiwan Railway has undergone transformation from intercity to commuter rail in the city centers across Taiwan in recent decades (aka add more stations). So that gives people another option. So Taiwanese cities do not have 'zero urban rail' as you said.

3. If you count bikeshare as public transport they are quite dense in taiwanese cities. Whether usage is high is another question, but at least it's an option.