I think the reason it doesn't expire is that the diving part of it all is considered to be a skill lesson like other dive certifications. If I were wondering about a person's first aid skills being up to date, I would ignore the rescue diver certification entirely and ask about the first aid.
Years ago, when I had only maybe 50-60 lifetime dives, I did a dive in Cozumel that featured a well-off middle aged executive and his new trophy wife. (They were at our hotel and we actually got to know them a little, so I know what I'm talking about with that comment.) She was newly certified for the trip. He, on the other hand, was a Rescue Diver, and he made sure we knew we were in good hands in case anything happened.
She was a pretty decent diver. She had very reasonable skills for a new diver, and she seemed to be having a good time.
He was a disaster. He was easily the worst diver I have ever seen in real life. The DM literally held him by the arm during most of both dives.