The fix for me, though, is to start in Safe Mode, then "Rebuild Database".
Then, start in Safe Mode again, and redownload and install the "Software Update" (mine seems to want to do it in Safe Mode but when in normal mode the PS4 says I have the latest system).
Then, my disc drive problems disappear for a time - mainly until I put a new game in and the game installs stuff on the hard drive or the PS4 downloads a game update.