Limited supply and security aside, the public ledger could do wonders for government spending transparency. Can you imagine if you could build a dapp for US expenditure? It would tear down misconceptions about spending and people might be able to see where the money actually goes.
Isn't Proof of Stake the literal implementation of the rich get richer though? I suppose Proof of Work is the same, but it's a shame that it can't be implemented another way. Every public consensus algorithm seems to collapse to rich get richer by necessity :/