- "I don't see what would prevent China from shooting down Starlink's constellation."

They absolutely do not have tens of thousands of anti-satellite missiles, or any other credible (non-nuclear) way to dismantle a constellation of that size. If you look at their own news media[0], they (Chinese defense) consider it a major weakness, and priority.

[0] https://www.scmp.com/news/china/science/article/3178939/chin... ("China military must be able to destroy Elon Musk’s Starlink satellites if they threaten national security: scientists")

- "Researchers call for development of anti-satellite capabilities including ability to track, monitor and disable each craft The Starlink platform with its thousands of satellites is believed to be indestructible"

There aren't tens of thousands of Starlink satellites over China, and I suspect the issue would be solved or escalated way before the whole constellation gets down.