I wish all Bitcoin h0lders could earn from network transactions and fees to be honest. Miners and big whales are the ones that benefit most from holding Bitcoin. Can you imagine if there was this idea that if we held Bitcoin we would earn a portion of the network transactions we would all benefit from the fees. So many new holders would invest in Bitcoin, but of course Bitcoin now has lost it's currency for the people feel.
it already exists and it is called Proof of Stake and it is a flawed way of distributing coins in my opinion because it is basically saying the rich should get richer and do that by performing nothing. basically sitting around and increasing their wealth.
with bitcoin and it s Proof of Work they have to invest and work to get paid! that is a much better design.
Proof of Stake Flaw was fixed by zeitcoin, by moving to an Ultra Low Inflation rate of .0005% per year.
This removed your rich getting richer flaw.

All Proof of Stake Coins, act as Full Nodes distributing the ledger and processing transactions by staking.
Bitcoin has yet to fix the ever increasing Proof of Work input costs require to run the network.
At some point, if the price of the coin decreases below production cost, the miners shut down and the network freezes.
Proof of Stake Energy Efficiently protects it from that scenario.