It would be interesting to have a "PoW zap". You can game Bitcoin zaps by zapping yourself, but Proof of Work costs the same either way.

If clients periodically PoW zapped the accounts they follow, legitimate accounts would accumulate huge sums over time, and spammers would always start very low.

On a cell phone? No problem! Someone could run a PoW zapping server that converts Bitcoin into PoW with server efficiency