Sure the load could be distributed to a p2p network, but how are you really going to prevent malicious users/nodes? It seems like it would be a nightmare to develop a fair system. A fair system where a user's post is actually propagated (included in mining) to the network and not silenced by a large installation that doesnt want the content on the network. It would seem that if youre using some sort of bitcoin system (or some derivative), a node would just need to contribute enough hashing power to exclude specific content that they don't like (or have been paid to exclude) a significant amount of time to frustrate users. Your centralized resources would always have to be able to provide more hashing power to keep control of the network. Seems silly to chase after big mining installs. Maybe I dont understand your idea... "Fix reddit with bitcoin! [[insert story about being let go and why what you were working on was actually valuable]]" doesnt really explain anything. Maybe this could be a good idea, but it just sounds like vaporware at this point.
Just create an altcoin that you have more control over. But I guess that no one (you?) would benefit enough, because its not tied to bitcoin's value being inflated.
Disclaimer: I own some bitcoin. So dont think Im just trashing on bitcoin.