Point of Contention,
In Proof of Work the coin's value really has no value as it has no reproductive capability built in. The Value is in the ASICS that produce the coin and allow it to function,
time has proven , and their value decreases every 2 weeks. As the small time productions have discovered , it is no longer affordable to be in an ASICS arms race.
At some point only 1 or 2 will control the asics, due to ASICS & Electricity costs.

Satoshi idea only worked before ASICS enter the scene, he did not foresee that, and that forever destroyed the idea of anyone being able to mine and reproduce his coin.
Proof of Stake fixes that PoW flaw, by placing the value of the ASICS inside the coin itself.
So all of the millions that get wasted on hardware , that is outdated in a year, flow into a coin that can be turned on every 20 days for a few hours and generate profit.

In Proof of Stake with a low stake rate, selling the Coins as Profit decreases your ability to make more, but can earn you profit on a continuous basis as long as managed property . You don't have to buy new hardware every year to get the same amount of Profit, in fact the more you hold the more Valuable you make the coin.
Another Reason for the Knights was to keep the amount of ZEIT split up , so that a handful never control the entire amount.

And in your point , the Rich get richer, is because a handful control the entire amount, but once they control it all and the poor and middle class have very little access to it,  they cause what we see in the US now,
The Poor will move to an Alternative ways of barter , and ignore the US$ since they have no real access to it and that also decreases the Velocity of Money.
example:https://en.wikipedia.org/wiki/Weimar_Republic

What the rich forget is their wealth is built on the poor and middle class like a Pyramid.

Rich Hoard the wealth as they are currently doing,
The Poor & the Middle class leave the system entirely finding alternatives means or currency to barter.
Which Now changes the Pyramid.


Some examples, The Car Manufacturers prices are so high , Poor people at best get a used car, next choice a Mope-head, or ride the bus and final choices
riding a bicycle or walking. This destroys money velocity , no car , no car insurance, no gas needed, which also hurts insurance companies , auto repair shops, and oil companies plus anyone that performs a support service for these companies.
And what all of these companies have in common , is they cut jobs which decrease the middle class & poor support of the rich even more, it is a downward spiral,
that results in the end of a FIAT currency, which is what we are seeing now.
NIRP (Negative Interest Rate Policy) will be their last failed attempt to save a dying FIAT system.

 

FYI:
The whole problem with the RICH is they act like a Parasite on a Host Body,
when they become too dominant of a host the host will die, and the rich along with it.
Farming is a good example, in the old days you used manure and tilled in grasses and wood ashes into the soil which fed the micro organisms & earth worms and this would increase the soil's fertility so your plants would be abundant.
Now they dump the cheapest of N P K only , and the soil is depleted of the micro nutrients which make healthy plants, which is why their input costs cause so many farmers to become bankrupt and your produce is less healthy every year.
Which less nutrients makes people sicker and frailer , I remember 65 years olds racing 8 and 9 years olds , just playing around.
Now a days most 40 years old people can't even run, the current parasitical system is on the verge of collapse and it is killing people we all care about in the process.      

FYI:
On your Point :
The algo i think was like steam from heated water.
The money flow up's and ends up in the rich peoples hands.
Problem is they hold it,
the Knights will be returning it thru Charity , Tithing , and in paying workers to achieve making this world into a better place and in other ways.
Therefore keeping the cycle moving until the Knights are no longer needed and the system maintains itself.