Taiwan is a tiny island, with relatively little international travel (compared to the US, China, etc). If they have no cases internally, and they seal the borders before those cases are introduced, then almost nothing else matters. Small, isolated, island countries can do this -- but even then (i.e. New Zealand) one mistake will mean rapid endemic spread. So sure, as long as Taiwan continues to effectively isolate itself from the outside world, they can probably carry on. But they're not going to: they're already talking about re-establishing travel with the rest of Asia.
It's virtually impossible for a country like the US to do the same thing Taiwan did. Even if we could seal the borders like Taiwan, our population is about 13 times larger, we have large land borders with other countries, and a proportionally large number of expatriate residents with right-of-return. Even with our bans on international travelers, the US has had 6.6 million foreign arrivals in 2020 [1]. Effectively 25% of the entire population of Taiwan has arrived in the US in 2020. And that's just non-citizens.
[1] https://www.trade.gov/visitor-arrivals-program-i-94-data
Yet, no lockdown.
No country managed the disease better than Taiwan. We should learn from Taiwan. See [1] for an analysis of Taiwan's response from early March 2020.
It is interesting to reflect upon why most countries ignored Taiwan. The World Health Organization's locking out Taiwan on China's request is probably one reason. Is it the only one?
[1] C. Y. Wang, C. Y. Ng, R. H. Brook, Response to COVID-19 in Taiwan: Big Data Analytics, New Technology, and Proactive Testing. https://pubmed.ncbi.nlm.nih.gov/32125371/
[2] https://en.wikipedia.org/wiki/Diamond_Princess_(ship)