I did, for a while, have a don't-care-if-I-break-it cheap camera with a lanyard that I used for this on group rides a few times.
But mostly I just fail to take photographs.
Pocket issues can be circumvented with recumbent-specific jerseys, those fishing/photography utility vests, bum bags, etc. On something like an ICE trike you can get a thingy to mount a bar bag off to one side of the seat. Or lightly-loaed banana bags can be rummaged in without spilling their contents.
Action camera on the bike doesn't seem like a bad idea, if you're after those kind of photos/video.