I still don't understand what "rare" means here, and I have not seen a case made that anything of value is lost. Why this is very bad?
Rare as in out of print? Rare as in only a few copies left, but nothing valuable? Or rare as in humanity is losing something?
Libraries and booksellers, used book sellers routinely throw away books that can't be sold, donated, or circulated. They are pulped.
For actual rare books you can digitize them without destructing them. Internet Archive has Scribe Workstation.