I don't see how verifiable CPU-only mining solves the processing power advantage in mining.  Pools, farms, and botnets can still be used get an advantage.

Don't you need to enforce a "one connection per person please" policy somehow?  If there's a mathematically rigorous way to do this of course that's the way to go.

I was thinking that the network might require a user to solve a capcha to connect and timing out the connection after a few hours (probably already has been proposed).  I know, this is terrible idea but it might be effective at keeping the mining egalitarian, which I think is what you are aiming at.