Proof of stake incentivizes low velocity of money - you have to stake to not have your funds diluted. This seems like the opposite of what the digital aspect of cryptocurrency should be bringing to the table.
And many people are "hodling" cryptocurrency as a long-term store of value anyway so presumably they aren't concerned with the velocity of money.
If your staking period is just a couple of weeks, this is probably less significant than owning a mining farm. But if your staking period is several months, the opportunity cost probably is greater than mining or hodling, because you sacrifice a lot in terms of flexibility.
Which, if you can still sell your staked coins, what is the point of locking them up in the first place?
Large existing expendable cash has a greater advantage to mine and mint. Mining pool operators are also in a position to manipulate minting and transactions in the network.
If doing so decreases the native assets velocity (for the sake security, finality, ease of sharding, etc), so be it.
So with lower fees, lower inflation, and higher throughput the velocity is more likely to grow significantly than decrease.
Using purchasing power (or more specifically an artificially constructed and highly manipulated bag of goods measure called the CPI in the USA) is a switch to obscure the rate of inflation, as if it couldn't be measured directly.
But Inflation always has been issuance, not purchasing power. Pretending otherwise isa tactic used by people who engage in inflation to try and obscure its effects (because purchasing power is affected by things like growth in productivity.)
Pretending like it's a measure of the price of goods is a political (not economics) tactic used by governments to obscure it-- because the price of goods are affected by other things--like increases in productivity, lower cost goods from overseas and the like.
Currency issuance is related. Is not the same thing
Economic models so far, however, suggest the reward needs to only be a tenth of POW reward.