I kind of like the idea of using Trash for its intended purpose.
I think the real problem is you are blindly backing up your entire $HOME
Add the Trash folder to your exclusion list. Better yet, add ~/.local to the exclusion list, since I can't really think of a lot of things you'd want to back up from in there!
I really do dearly hope you aren't backing up ~/.cache too because that would be terribly foolish...
...
If you are deleting many books at once, calibre warns you that they will be permanently deleted (it's faster than moving to Trash).
IIRC there is an option in the delete confirmation dialog to skip the Trash.