I know someone who is similar with the paper files, but lazily sorts them when she needs to retrieve something, so the full scan only happens at most once.
This is pretty efficient. She lazily sorts them on first access. They are stored in a thunk and then lazily evaluates them. After that repeated access is efficient.
Even better is to scan and pitch what you can during the scan, then file what's left. Scanning for computer search is awesome.
What do you use? I have an awesome document scanner but Acrobat Pro takes like ten seconds a side to OCR with a ridiculously single-threaded process that ends up taking minutes to finish even short documents on a monster workstation.
Not the person your question was to, but: I use Paperless myself, but Mayan EDMS is another option. OCR kinda sucks as a rule, but it's better than the big ol' firesafe I used to have.