I still put optical drives in my workstations. I like to run linux liveCDs on WORM media for secure web browsing or checking the contents of hard drives I don't trust.
I also still burn discs. Maybe 10-15 a year. They're mainly for liveCDs or moving files to suspect computers. I don't use them for backups.
I probably burn a lot less than that. I never bought a BD burner, because I've long-since accepted my conclusion that HDD for backup of large data quantities is better; my server keeps all my client workstation drives backed up; and I back up the server. I don't need a blue-ray player, or haven't wanted one enough. So I stuck with DVD burners for building my most recent systems.
For that, a good DVD-burner can be cheap enough -- maybe no more than $25. So I've been in the habit of equipping every system. That habit replaces the long habit of installing a floppy drive in every system. I only jettisoned floppies from my equation for about the last five years, and I made sure to keep the old ones -- some dating from the '90s -- because they were becoming hard to find and (see "Hoarding . . " - - "you never know when you might need one."
A long, long time ago, I had done an econometrics project using a software package named "RATS:" "Regression Analysis of Time Series," and "Gauss," which allows for building your own statistical procedures (provided you understand the math to begin with). I saved all the text, data (in ASCII) and graphics to a 5.25" 800KB floppy. Later, I wanted to look at that stuff, and I had the floppy -- but I'd long since discarded those drives -- probably should have transferred the files to newer media before then.
I think I still have a small library of 3.5" floppies. And I'm suddenly aware that I only have one system in the house fitted with a drive to read them, and only one other machine with a motherboard old enough.
You always need occasionally to burn an ISO. If you shop for budget software, you'll more often buy either retail or OEM packages with a DVD install disc. If you want to play certain games or run some various simulators, you need to either use the original install "Disc 1" when you start the game (to prove valid license), or burn the extra permitted copy which would allow you to go from one system to another and "play or simulate."
The annoying thing I feel about USB thumb drives is their non-standard size and shape. It would be nice if they were more easy to label, and nicer if they would all just snap together like dominos glued side-by-side. So far, I just keep USB flash drives with important data, installs, utilities and formats inside a little mahogany box, and I have to fish through them to find what I want or need.
If you think about it, 3.5" floppies or optical discs (either CD, DVD, BD . . . ) can be stored like the Dewey system card files at a library. I still have about six double-drawer optical disc cabinets, two more long "boxes" with slats I bought at IKEA 20 years ago, and similar drawers for the 3.5" floppies.
I've also more recently discovered that you can now assure yourself of bootable access to an external optical USB and possibly eSATA optical drive. It was once the case of an uncertainty whether you could boot from such a drive: it would depend on the hardware. But for some time now, it has been a fairly reliable solution alternative to building every system with an optical drive.