The question is: What is more likely in 1000 years to still exist and being readable. The papers caught in some lost ruins or some form of storage media?
Sure, as long as the media is copied there is a chance of survival, but will this then be "average" material or things we now consider interesting, only? Will the chain hold or will it become as uninteresting as many other things were over time? Will the Organisation doing it be funded? Will the location where this happens be spares from war?
For today's historians the random finds are important artifacts to understand "average" people's lives as the well preserved documents are legends on the mighty people.
Having lots of material all over gives a chance for some to survive and from 40 years or so back we were in a good spot. Lots of paper allover about everything. Analog vinyl records, which might be readable in a future to learn about our music. But now all on storage media, where many forms see data loss, where the format is outdated and (when looking from a thousand years away) fast change of data formats etc.
