But then miners get cheap reputation.  Miners can collude to upvote each other.  You also need negative ratings (aka antizaps) for an optimal reputation system.  Opentimestamps have the issue of who stores the data.  Reptuation has to be able to evolve, rather than be a static timestamp.  

This popped up in the last few days, which may have some promise.

https://github.com/cromatikap/nostr-reputation-authority 

 They don't, like openstamps it's all hashed into one big transaction. The miner could make the Onchain transaction with the tree cheaper, but that just benefits whoever is running the rating server.  

 Who runs the rating server?  Who pays for that?  What if the miners run the rating server.  And so on...