Nope. Sorry.

1. Mining is made like this to make blockchain safer, not to share easy money around.
2. What happens if miners go in and out, will they ever lose their place in line?
3. You logic seems to see the same, no matter that there's a 1kH/s or a 1TH/s miner.
4. What happens if some miners make a software allocating themselves billions of different "IDs"? I guess that it will be only them mining and the others waiting their "fair turn".