Limited patriot missiles may not hurt the US too much in a war with China because China will likely overwhelm patriot batteries, and destroy those batteries in one day. Without batteries to fire the missiles, the missiles are useless.
One reason the US does not build that many missiles in a year is because the fuel in missiles degrades and makes the missiles too dangerous to fire, meaning, if we build a whole lot during peacetime, most of the missiles will go in the trash along with the piles of money it cost to purchase them.