We would also disenfranchise actual citizens if we did that.
How do you figure that?
If you havent figured this out, with modern day tech, we can digitally ID people through either facial recognition technology or just looking the name given up and matching it with image on the screen.
Or if you insist on physical IDs (which are actuall a but more insecure.) you could have them be sent out to those who need them for free, given they fall under a certain bracket.
But I still recommend the first move because its cheaper.
This isnt as big an issue as people make it out to be.