Then there would be unfilled jobs for firemen, which would increase the wages for firemen, which would prompt more people to move into a career as a firefighter

Then there would be unfilled jobs for firemen, which would increase the wages for firemen, which would prompt more people to move into a career as a firefighter, which would increase the supply of firemen until the jobs willing to pay the new prevailing wage were mostly filled, approximately. That's exactly how pricing signals work. "Firemen" is not a fixed set of people.