Gym shorts, technical running shirt, sure you've got jerseys but sometimes a random combination has no pockets. And if you ride somewhere to run, or to a gym, chances are you aren't wearing a cycling jersey.

I personally prefer the smallest seat wedges and they don't really have extra room for keys. I could cram them in maybe but it would be a pain AND, once or twice in enough rides I have accidentally left one not fully zipped and dropped small items from it. I wasn't kidding, I put netting on bottle cages, usually storing my sunglasses there. I can stuff gloves there, rain jackets even, coins. The netting keeps things from bouncing out, and of course a bottle on top locks everything in. It is, IMO, an effective, unobtrusive and convenient solution to OP.