My understanding is that there are specialized copy devices that can do a decent job of bound volumes. But to the basic point...
Paper takes up a lot of space. You can't keep physical copies of everything forever. It is unfortunate that it seems as if film and poor quality scans replaced physical copies in some cases too early. But libraries do run out of space, especially well-indexed space.
I suggest you walk past a paper mill sometime to truly understand how environmentally horrific they are. The one up near me finally paid to put scrubber systems on their air exhaust. Before then when the wind was blowing the right direction it made all of north portland smell like rotting cabbage. Even with the scrubbers you still smell it at the airport occasionally.
Another fun detail is the parking lot workers park in has a drive through car wash/rinse device. The employees use it every shift when they leave... or at least they should if they don't want the acid fumes to eat the paint off their car.
Paper mills cause far more pollution than any potential carbon sequestration benefit, which would be temporary in the long term anyhow. Books will rot unless you put them in a controlled atmosphere.
I don’t know nearly enough about the process to challenge your point, but I want to point out that just because something smells bad or produces acid in huge quantities doesn’t mean it’s permanently bad for the environment like unsequestered carbon emissions.
The dose makes the poison and pretty much everything is toxic to a local environment at industrial scales. If the acid is stripping paint from cars faster than parking it on the beach, you can bet its a problem for the vast majority of an ecosystem that evolved alongside a freshwater river.
I'm not suggesting we make extra paper just for the purpose of sequestering carbon. The would obviously be foolish. All I'm saying is that if we are going to keep printing newspapers anyway (and at the moment we are) and the paper that goes into them is a sunk cost, then it might make sense to keep them around both for their historical value and as a carbon sink.
But my tongue was part-way in my cheek when I suggested this because you'd have to warehouse an awful lot of newspapers to make a dent in the carbon problem.
Actually, that's a specific thing that does not work (at least long term). Trees die and rot if not cut down, and the carbon from that process has to be absorbed by the younger trees growing in the same space. So once a (mature) forest exists at a given location, it will no longer absorb any more carbon unless some of the trees are cut down and used for something that doesn't allow their carbon content to return to the atmosphere.
Paper takes up a lot of space. You can't keep physical copies of everything forever. It is unfortunate that it seems as if film and poor quality scans replaced physical copies in some cases too early. But libraries do run out of space, especially well-indexed space.