- Is it a major reason for Chinese interest in Taiwan?
TSMC is not the most important reason for Chinese interest in Taiwan.
This controversy is a legacy of the Chinese civil war (1927-1949) when The Kuomintang (KMT) and Chiang Kai Shek's followers fled to Taiwan to avoid being exterminated by Mao Zedong's CCP and their followers.
- Considering possible Chinese intervention in Taiwan, would getting control of the industry (or whatever would be left of it) be an important argument for the intervention?
No. Because to have military involvement, the USA has to show the international community that something grave is taking place, which is a threat to humanity and Western interests.
Saving a company from a Chinese takeover isn't a good selling point. That is why the USA is masking it as the preservation of freedom, human rights, democracy, etc.
If so, why wouldn't Taiwan commit to destory all the factories and knowledge in case China tries to occupy the island (so as to decrease the probability of intervention)?
Because this is not a good idea.
Taiwan's expertise in semiconductor manufacturing is a national pride and the result of decades of hard work of Taiwanese highly valued human resources and the Taiwanese government.
Consider the Canadian Avro Arrow program. They scrapped the program in favor of the US Bomarc missile. Consequently, Canada remains a US vassal and a permanent US defense customer. On the contrary, a much smaller nation like Sweden is a self-reliant country in the defense sector.
- Is the industry an important factor for the US to support Taiwanese independence, or they do so mostly for other reasons?
The semiconductor industry is the most important factor right now. However, even if that was not an issue, the reunification of Taiwan will give rise to other problems for the USA:
- US defense export to Taiwan will cease.
- The strategic US naval advantage around Taiwan straight and in the South China sea will go away. You can consider Taiwan as a permanent aircraft carrier.
- Although this is a minor problem - Taiwan is a part of the supply chain of the US aerospace industry.