Simple naive economics suggests otherwise. If a 10% domestic requirement keeps demand artificially high, competition will enter the market. New factories, etc. will spring up to get a piece of the fat. They will compete on price, quality, etc.--all the usual points of competition. People will get creative to get their piece of that pie. (Of course some of the creativity will be figuring out ways to subcontract it to China and still count as American.)
I mean you got the naive economics part right. These kinds of contracts are selected based on relationships, not product quality or even business acumen. In your mind the government conducts regular technical product evaluations of every small business that attempts to make masks at scale? That isn’t reality.
They are saying each individual hospital would have to choose a domestic manufacturer for atleast part of their supply. This would cause more domestic manufacturers to start up and compete for each hospitals business. The rule would affect the hospitals directly, not the mask makers.