^It's just caching the print jobs for network and print queue efficiency. Biggest advantage is that it eases network congestion because multi-copy print jobs get sent once rather than as many times as you need copies. It also frees up the sending PC by not making it's print manager keep polling the network to see if the office printer is ready to accept the job. In a small office, onboard RAM is usually sufficient to handle this function. But for large document or 'high traffic' situations, hard drives are (currently) a much less expensive and more efficient way to build a print queue.
Caching allows you to prioritize or delay print jobs. You can set your print job to run at a lower priority or after regular office hours if you want to. That way, the office football pool sheets don't get delayed because some dork in accounting is frantically rushing to get 5000 pages worth of subpoenaed financial data over to the SEC by close of business!
Caching also comes in handy when you have a paper jam. Most good printers (and copiers) have the ability to recover exactly where they left off. Nice for when you jam up on page 275 of a 280-page job and you don't want to resend and reprint the whole schmeer
Another big advantage is it separates the print job queue from the actual print function. Network data flows at megabytes per second. Paper prints in pages per minute. Caching lets people pile jobs on the printer's drive, after which the print engine does its best to get it all done. (Often by working through lunch break and staying late.) It's an obvious idea when you think about it... Bosses have been doing the same thing to their employees since the dawn of bureaucracy.
Most copiers and printers don't maintain archives of files unless they're set up to do some sort of low-end "print on demand" function. Some offices will do that so they can generate paper forms and handout sheets as they need them. Much easier than having to hunt down a form somebody desperately needs when the office manager is out for the afternoon. Again!
So the fact these gadgets don't completely erase* old print jobs is a side effect rather than a feature - or a conspiracy. Think of it more like forgetting to shred paper documents before you put them in the dumpster.
*Note: it's a pretty well known fact that most computer systems don't actually erase
files when you tell them to. What they do is mark the disk sectors as being available for reuse by new saved files. If it were a library, that would be the equivalent of cleaning out old books by simply tossing the catalog card and telling everyone they were gone. These 'deleted' books, however, would remain on the shelves until somebody needed the space and got around to actually tossing them.