There's a time problem, a data storage problem, and a general security problem with using paper instead of hard drives.
Time: To use paper, budget time for printing every document modified during the day, filing each paper copy, putting the drive in the wiper, wiping it if you're supposed to stay watching it, retrieving the papers from the file, scanning them in, and editing OCR errors, which ideally should be rare because you're scanning a fresh print but they still happen and it's very important that you don't order the 15l part when you need the 151. Compared to removing the drive and locking it up, that's probably at least an hour of extra work, which means a lot less gets done each day.
Data storage: You're doing this so the sensitive data isn't on the drive, and in order to do it, you're putting the same data through many other systems that could theoretically be used to try to access it. Sure, probably nobody is going to break in to try to get copies off the printer's cache, the scanner's cache, or to modify the wiper to read before wiping, but anything is possible. Also, I've assumed that you have a data drive that you're wiping and a system drive that you're not, mostly because if you only had one drive then reimaging a fresh version every morning would extend that time problem to ridiculous levels, but if you do, there's a chance that some parts of the data files will be on the system drive in temp files, so you'd still have a hard drive to secure. More points where the data is stored won't make the process worthwhile.
Security: Locking up a hard drive is no more complicated than locking up papers, and in fact you can use a smaller box to store it with less risk that someone will get it. Among other things, you don't have each day's stack of paper to deal with. It will probably be shredded, but never having been printed makes it even harder to reconstitute. Paper is also easier to steal. If I, your colleague who's also a spy, manage to get into your office while you're in the morning scan process and steal some of your sheets from the already-scanned pile, then you might not notice, allowing me to sneak your documents away, and if they get caught any time after I drop them, you get the blame.