This works fine for small teams but for larger (and with large, older codebases), the ramp-up time for being an effective support dev becomes a drag because it can be months between support stints. We don't all have eidetic memories and forget the tricks we use to diagnose production issues.
To counteract that we've recently put a developer on a 6 month rotation, and support them with a rotating backup. This allows the primary support developer to not only stay productive fixing issues but also surface intelligence around the problem areas in our app (ie: what's always needing support) and construct tools to make resolution easier or better yet convert to a self-serve.
I infer from your comment that you're a smaller team so perhaps you won't need to put someone on a long stint, but you might want to consider doing so anyway in order to have a resource pave the proverbial cow-paths and make it easier for the team in the future.