That's not quite true.
In my zip code, no one was able to get the 'bama phone. My friend in Colorado wasn't able to get one either. We figure that it was because those phones don't work in our areas. We live in the dead zones. Landlines work great!
Look at your state ID or DL on the back is there a barcode on it if there is that’s gonna be your covid pass the amount of coding to link the states real id compliant biometrics to a vax data base is likely to be a few thousand lines easy peasy for a competent coder. If not simply printing out a individual unique QR or 3D barcode at the county level to issue via mail or in person at say the county tax or municipal courts. To think that someone could say oh I cant get a digital print out in todays world via mail, or at a local government office is delusional. The county is doing the vaccines they surly will issue QR cards on request just like voter id cards or tax statements or any other of hundreds of kinds of local government correspondence. Everyone will have access to either the QR code app or a issued hard card it’s not that hard you likely have a county issues voters card the vax card would come off the same printer and mail system.