Are they really that robust? Was I just storing them stupidly maybe? Or maybe it was because all the ones we had were used ones from work.
Not very. There's significant wear and tear from the drive head, to the point that you could see it with the naked eye after a while.
If you are not using them frequently, storing under ideal conditions, than maybe. I've been able to read floppies a decade after they were written. Not for long though. Drive required cleaning afterwards too.
Certainly 5.25" floppies from the late 80s and early 90s were nearly bulletproof in my experience. 1.2MB was a bit flakier than the 360KB though. All were still perfectly readable 20 years later, though at this point they all got thrown in the bin due to their obsolescence!
Of course, back then I knew enough to spend a bit more on the good quality ones, so that could have something to do with it.
CDRs are next level in terms of unreliability. Last year I discovered that almost none of the CDRs I'd burned in the early to mid noughties remain readable: simply had to destroy them.
Eventually, sourcing replacement media and drives.
Was it secure? Yes.
So, what's the problem? Updating 30-year-old gear with media from its era seems to make sense.
If they were really wedded to digital media and needed to bridge that gap, Sony used to make a floppy disk that you could jam a memory stick into and it would read in a normal 3½ inch floppy drive. Very cool gadget.