What was Satoshi trying to solve that he, as many who contributed to what eventually became Bitcoin, felt was the root problem with fiat money? Trust, as a consequence of two things,
1- Centralized, focused issuance and control of money supply and monetary policy
2- Trivial cost of issuance
While issuance entails no cost, the money remains at the mercy of the basest of human qualities, self-seeking greed. All corruptive tendencies of fiat money are a direct consequence of the trivial cost to issue infinite money.
Satoshi's proof-of-work algorithm solved for these two flaws by implementing an ingenious cost of creation/issuance algorithm that keeps every actor honest and perpetually scales in proportion with Bitcoin’s value as a monetary network —the higher bitcoin's value, the higher the cost of issuance, and vice versa.
Proof-of-work requires those who acquire the new supply of money (miners) to continually input real-world work and cover recurring operational costs, ensuring that those who receive the new supply of money cannot keep hoarding it at no cost to themselves. Miners are forced by the game theory embedded into the protocol to redistribute bitcoin into the market.
Any system where the creation of money entails no work and cost would be fiat 2.0 all over again, a system where wealth equals power, where the rich forever get richer and the poor get poorer.
In proof-of-work, wealth != power
Miners input work and recurring costs to find blocks and receive compensation for their work, however, the blocks are validated by full node users, not miners. Full nodes enforce the rules — accept/reject blocks found by miners — and hold the power to keep miners honest. Proof-of-work admits of no corruption or privileges.
Proof-of-stake is a regressive hermetic system abstracted from any interface with the real world that walks back on Satoshi's solution. Those who receive the new supply of coins are not required to undertake any work or suffer recurring costs to themselves (trivial cost of issuance).
This causes the new supply of coins to be inevitably hoarded by those who receive them (large stakers), thereby leading to a concentration of wealth similar to the existing fiat monetary system (focused injection of money), and since in proof-of-stake, wealth = power, large stakers/preminers effectively assume the role of central bankers, acquiring all the new money and perpetually amplifying their power over the network.
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