In roman times I see one area, were the demand is obvious: jurisdiction. All edicts or decisions of the imperial court (a consilium principis) were published on wooden or bronze tablets at a central place in Rome. Same with decisions of the senate. IIRC it was published at a wall of a temple. Some of them were copied and sent to all propraetors which copied them again for all 2000 city magistrates of the empire. Also lots of lawyers needed a copy all over the empire. The roman iurisdiction was less based on laws but on precedents or leading cases. Not just decisions of the imperial court, but also decisons of the praefectus urbi or the big quaestiones in Rome led by praetors.
Lately I have read an article about the press in Rome. Of course it did not exist in a modern sense. But nevertheless some guys operated a kind of press business. They wrote letters frequently to hundreds of friends in the provinces. These letters were almost identical and full of actual news about the capital (politics, gossips, ... everything). Something like subscribing to a frequent newsletter.
The army, which was already mentioned above, was the biggest buerocracy of the empire. Actually the civil administration of the provinces was operated mainly by the army or personell of the army. And the army knew a lot of forms as Konrad Stauner and others proofed. Not that much standardized like nowadays, but clearly standardized. Unfortunately the army used whatever material was available onsite. So again we need mass availability of paper that the army sees a need for printed forms.
Regarding literature I am rather sceptical. The roman society was less educated than people think. The upper classes (senators, equites and decuriones) were very educated, but thats about 500.000 people of 40-80 Million. Plus many slaves operating the private and public offices were very educated. But the big rest was most probably either analphabets or bad readers/writers with not more than 3-4 years school, and even this not consistently.