Can common folk get repeated tests or everyday testing for the coronavirus? Can they get antibody testing regularly? The answer to that question is no. In NY, you have to schedule an appointment at a predetermined location. I know that because my mom is an essential worker on Long Island and there is a website (covid19screening.health.ny.gov) to schedule a test.
Normal folk have to go to work if they are deemed essential even without daily testing. MLB players and personnel presumably won't and will force MLB and/or the owners to pay for that in the process. That's not something you and I can do or can force our employer to do.
What part of availability is so hard for you to understand?