So the fight is cast as one between local and national governments. If the Library were nationalised, then the military conflict would have to end. Wasn't the cause of The American Civil War a conflict between federal and states' rights?
There are some internet posters who questioned why the LTF doesn't fight harder against the MBC, or allow them small victories. This becomes a lot more understandable when one realises that the LTF is significantly outgunned and outnumbered by the MBC, and that if they attempt to escalate, the MBC can easily ramp up their forces and curbstomp them. We see this in the final story arc of the third novel, where the LTF is losing hard against the MBC in a straight up battle.
The MBC is a division of the Japanese Justice Ministry. As such, they can get the budget needed for recruits, guns, ammo, gear and vehicles.