The tests are free to the person testing. They don't magically appear out of thin air. The government is buying them via the normal capitalist system but there aren't enough because the manufacturers can't make enough to meet demand.

(In part, because major manufacturers closed factories and destroyed inventory between spikes. https://www.nytimes.com/2021/08/20/us/abbott-covid-tests.htm...)

I'm a bit baffled as to why the Defense Production Act hasn't been utilized more during the pandemic for stuff like this.

Are PCR tests free in the US? I found tons of paid testing services when looking, they just didn't have capacity.

Because one of the options you stated (waiting in line) isn't even an option in a lot of areas.

This specific scenario has nothing to do with market theory. It's a combination of regulation, subsidization, and infrastructure. We're not buying playstations.