I was at O'Hare once, several summers ago, when UA's computers were "down." E-tickets were new, and relatively rare. My ORD-MCI flight was boarded only with paper ticket customers (my upgraded FC boarding pass had been issued earlier in BOS, thankfully). Gate upgrades were not permitted. E-ticket people were left behind. (UA simply told them to go to ticketing in the terminal -- there they waited for the computers to come back "up.")

Nowadays with 50%+ e-ticket holders, the airlines could not leave such a large group behind, so there must be some method to allow them onboard.

I am a paper-ticket adherent for many, many reasons.