I think we're using different words to say the same thing: "fixing access" is the same thing as increasing supply. Supply doesn't mean "you have stuff sitting in a warehouse" it literally means "made available for sale."
Yes you can do this with regulation (e.g., no hoarding, no price fixing, etc.) in addition to making it easier to produce new things. Which is what I think was being indicated there?
Sure $7.25 is low... but I don't know the last time I was anywhere that jobs were paid that low. Around where I live nobody will take a job for less than about $14/hour (maybe I saw bagging clerks at the grocery store for $12?), and that's even higher than our state minimum wage.
Because of that, minimum wage isn't the biggest problem anyway; the real problem is the part-time benefits cliff. Instead of saying "full time is more than 30-whatever hours a week" and then having benefits laws set against part-time vs full-time, or based on size of company, they should just be "all benefits are required at any employment level, they must be no less than 10% full-time equivalent, and can pro-rate to 100%, 100% reached at not less than 30 hours per week" and "no less than 10% of the 'large company' amount, prorated to employee count, to reach 100% at not more than 50 employees" or something.
Breaking health care insurance from employment would be a massive game-changer for employment law in the US, but I just don't see that happening in my lifetime at least.