Yes it would need a hard fork - but Bitcoin community is notoriously resistant to change, so it probably would not happen for some years or decades.
This specific example works and is economically rational because miners could make a PoW block and get its reward, or they could make the no transaction attack block and get its reward, plus the reward on NewStakeChain for submitting the proof.
Why would nobody be mining OldChain? You can't remove the block reward or change the difficulty without a hard fork. PoW miners would still decide which blocks are mined and reap the rewards (block reward and transaction fees). You haven't actually proposed a solution that wouldn't require a hard fork.