I also thought about that. But then, there is a bigger problem, because you need some way to implement mining. So, I can see two options: hashing each message separately, or implementing a hidden chain. I prefer the second, because then all hashes could be hidden as commitments. Then, the only option to stop that, would require banning all ways of encrypting anything (or pushing any random, non-explained data), which is hard to enforce.
Could you elaborate a bit more about this idea? I'm not understanding neither of the two options...