Answer: It's a combination of hardware and firmware.
That may be; I don't have multiple iPhone devices nor evidence to make this determination.
I am happy to report, however, that the problem with the camera not saving pictures was corrected after I did a restore as a new phone (not restoring the backup). A destructive "restore" - of course, I lost notes (I emailed them to myself before "restoring"), settings, passwords, et cetera. I had to re-configure a number of things, but the camera app saves pictures now. I will monitor the device's performance, in case some other functionality is affected.
This is not a solution, only a workaround, and a very unintuitive one ("restore" does not actually restore).