Would it be theoretical possible to restrict the GH each miner put into the System?
No.
There's no way to reliably determine how much GH a miner is adding to the network, therefore you can't restrict it.
IP restrictions are easily circumvented. Identifying each miner by a unique ID would require a central authority, which would make the whole system moot.
These are also the reasons why PoW was conceived in the first place -- every other approach before it was either centralized or insecure. (PoS, amongst others, being an alternative approach to solve the same problem)