That doesn't sound like too difficult of a feature to add to a media server. Just generate a playlist instead of picking the next thing on demand. Could add constraints like "choose show at random but select next sequential episode of that show from the previous one shown" or "fully random but do not repeat anything for x time/things".
Makes me wish I had that stuff set up to experiment with.
I've been pondering how to do this on my home server for a bit now. Haven't put any effort into the actual coding yet, but the thought is there. Maybe searching for a solution isn't that terrible of an idea.