Coin days is not flawed. If you have 100 coins and let them age for 10 days, you have ten times as much stake as someone who has 10 coins and let them age for 10 days. Compare apple to apples, not oranges.

1. Then people can just keep reusing stake.
2. Cryptocurrencies needs to be decentralized. You can't identify who one "miner" is.
3. See 2.