Jittered exponential backoff. You don't want the whole herd to come back at the same time, you have to add timing jitter to the clients.
I suppose the main reason I think it might be a bad idea, is that it would add complexity to the reverse proxy (i.e. now it's having to track whatever thing is being used and that complexity itself becomes a potential failure point...)
(To be clear, the clients should have their own backoff procedures, but I'm thinking about cases involving naughty clients, which are sometimes a harder problem to correct for...)
“Adding complexity to the reverse proxy” is kind of the central feature of service meshes, but the point is you pick one that’s battle tested and solves more problems than it creates.