Taiwan has not eradicated the virus. Their quarantine systems are good, but not perfect:
https://thediplomat.com/2021/01/taiwan-tightens-pandemic-mea...
While they have certainly come closer than most places, the downside of this approach is that it comes at a debilitating economic cost (edit: for most countries...Taiwan specifically may be able to get away with it for a while because they're a manufacturing hub), and literally any minor slip up can lead to the virus spreading like wildfire through the population.
Again, considering the vast differences in scale and complexity here, it's pushing the bounds of credulity to claim that the United States could do something similar. Even a "science-following" state like New York can't conduct a quarantine of remotely similar strictness.
Pretty much the only equivalent thing the US might have done would be to stop all immigration in January. Neither political party would have supported such a thing.