The caveat is that I've never actually spent time in a prison, my understanding of the setup is that the base level experience is that you stay in your cell / rec room, and can go outside to the yard like an hour a day. Beyond that, you can volunteer (or get paid some small amount) to help out in various ways, like working laundry, barber shop, kitchen, library, etc. I don't think any of these pays minimum wage. Adding another thing that prisoners can opt into doesn't seem crazy or exploitive, if it is truly just another choice that they can make.
RA's are not forced by the state to spend all of their time in the dormitory.
The state has chosen to imprison these people, it is forcing them to live inside the prison. The costs the state incurs in maintaining the prison are not "paid room and board" for the inmates.
Whatever crime you were committed of did not carry a penalty where you had to pay for your housing in prison. So your room in board is covered in the case where you work and where you don't and can't be deducted from wages. Now, the crime you were convicted of may have required you to pay some form of victim compensation. This is often deducted from any prison wages.