Yes of course as you say it can be done through identities. But then you have something very different than Satoshi's idea. You have a system where every single person on the network must be identified. Of course a system can be designed that puts limits based on identity (distribute mining rewards evenly, only allow one address per person), but then you have no privacy. Also this relies on the idea that no one can spoof someone's identity through whatever identity recognition system is used.


The reason Satoshi used PoW is because you can't spoof processing power. And of course he wanted to avoid the hassles and issues involved with identities.