> the sole reason why...Strong disagree.
1. The USA's current stance toward Taiwan is largely a continuation of its historic stance, which had absolutely nothing to do with semiconductors.
The USA currently maintains a strategic ambiguity wherein the USA sell arms and also remains capable of providing for Taiwan's defense, but provides no specific defense guarantee. That basic stance has been US policy since the 1970s, long before Taiwan became a semiconductor powerhouse. The Six Assurances were communicated to Taiwan about half a decade before the founding of TSMC.
2. TSMC and Taiwan are enormously important to the economy of the United States. The economic damage caused by loss of chip supply would be a major economic event, leading to simultaneous rapid goods inflation, massive equity draw-down, contraction in the real economy, etc.
At least in the short term -- 1-2 years after invasion -- domestic unrest due to the economic damage would be far more disruptive to the USA's capability and willingness to go to war than chip supply in the defense industry (the DoD, through a combination of reserve supply and substitution, would be able to operate effectively for many years without new chip supplies).
The military's need for TSMC-manufactured chips certainly provides a more hawkish hue to the USA's ambiguity, but it's far from the primary reason for USA's backing of Taiwan.