Equipment: Brother MFC-8890DW and Brother MFC-9320CW
I suspect it will work on: All older printers with Big Sur!
On upgrade to Big Sur, I found that my 8-year old expensive Brother MFC printers would no longer work, and that Apple was recommending that we use AirPrint. I could install the printers using macOS v10.15 (Catalina) (or older) drivers, and my scanners would work, but not the printers! AirPrint would not work either.
I scoured the web for many hours and tried 1) Resetting the printer system - no go. 2) Reinstalling CUPS (with SIP disabled and Gatekeeper disabled - no go because of Apple's read-only /usr filesystem ... not getting into setting up remounting the root (/) filesystem because of FileVault problems.
I noticed that this was a problem that everyone was having regardless of their printer brand - indicating that it was a system problem.