1) the gatherer are accumulating stakes but based on what? a coin address? IP address? How these cannot be hacked or lost in case of changing wallet for example.
Gaterers are p2p nodes so they are based on IP addresses. They don't belong to common users but the miners so changing wallet doesn't affet their ownerships.
2) I do not agree that POW is useless. Your solution do not imply any specific efforts from the miners, they are mining nothing, they are only generating blocks... there is no difficulty and no cost of it, so why are they still useful? Block could be mined by anyone running a full node, like, the gatherers or the users? Voting is not "time or power consuming", it costs nothing. So rewards are for doing what?
That's the character of proof of stake isn't it?
3) The accumulating stakes are doing basically what a stratum pool is doing, you embed the functionalities into the blockchain and into the wallet.
Partly correct. But it is limited. Please refer to "chapter 5. Security".