Why? Assuming people thinks that China will invade Taiwan just to take over TSMC, then what?
1) TSMC doesn’t build the tools that builds the microchips. In fact, they probably don’t even know how to build it, or even know the optical science to research and develop it. That dubious honor goes to ASML, and some other Japanese companies. But ASML, the euro company is currently in the lead for 5nm. TSMC just knows how to use their machine, and to get better at it. And to be clear, ASML doesn’t know how to manufacture the chips like TSMC can, so both companies need each other, in a symbiotic type of relationship.
2) In the event of war, then the losing side can just bomb TSMC factories. Then everyone is screwed. No more advanced microchips for anyone.
3) If China succeeds in invading Taiwan, then the USA will just force ASML to stop selling their equipment to China, like they already do now. So, China is back at square one. They might have the current technology, but no ability to advance to newer technologies.
The only viable solution for China, is to build their own chip making tools, and fabrication factories. Thus removing ASML and TSMC from the equation completely. Also, they will gain independent Intellectual Property rights and patents to their own indigenous R&D.
The American government is apparently thinking that China doesn’t have the skills to do this.