It is so terribly insane that this isn't done. You are being held by the state. The state has elevated access to state services. How easy would it be for them to hook into the state ID/DMV system and print you a state ID or driver's license before you leave?

If they can't verify your identity while you are in prison, then what are you even doing there?

All they did before I left prison was try to sign me up for Medicaid (I'm not elligible because I'm an illegal immigrant).

They did kindly let me keep my prison ID when I left which has my photo on it and says IN CUSTODY in giant letters. (they used to say INMATE but that word has gone out of fashion and they couldn't think of another word to use on the badges)