What is the reason that the new coins should be given in proportion to existing coins, iff the holder also does some work?
If the work done is equivalent for 1 and 10,000 coin holder, should the reward not be also?
This is hard to arrange. A rich miner with 10,000 coins could split their holding into 10,000 wallets of 1 coin each, and present to the network as 10,000 poor miners, and there-by get 10,000 times the reward.