It won't. It requires a hard fork and Bitcoin will not hard fork for DarkSend, nor jeopardize regulation issues.
It doesn't require a hardfork if the coinjoin organizers aren't paid by block reward, but instead by those they are coinjoining for. Or better yet, it would be decentralized and no one would be paid at all.
Misbehaving nodes don't get payment. So false.
The reason PoW works so well is because you can prove it. You can say "hey, here is the block header I have and here is it's hash. As you can see, it's hash is below the target, therefore I have created a block".
Coinjoin organization is a series of messages. You could (A) have a central authority see if the masternode is facilitating coinjoins and keep a log of behaving masternodes, or you could (B) just trust that the miner is right about whether the masternode was behaving at block X, or you could (C) trust your peers. Option A invokes trust in a central authority, option B allows miners to pay themselves (assuming they're operating as a masternode) every time and option C opens you up to sybil.
TL;DR PoR is an oxymoron because you can't construct a proof that you are offering a resource.