The problem is that such a perfect currency would never catch on, because 95% of crypto is about speculation for "moon". If you build a system that doesn't allow to dream about the moon, but is simply a good stable currency, nobody's going to "invest" in it, and it wouldn't take off.
It constantly boggles my mind why people never grasp the basic understanding of the 2 levers of value: price and quantity.
If I have a quantity 10 of something that is worth $1 then my total portfolio = $10.
If I still have 10 of them and they are now worth $2/ea my portfolio = $20.
Wouldn't it be the same situation if I had 20 of them still worth $1? Isn't the ROI the same, but now has the added benefit of their utility being easier (psychologically) to spend since I'm not worried about the cost of my dinner doubling before the dessert arrives?
Ah, I saw the monetary creation from a PoW point of view, while you see it from a PoS point of view. But this is somewhat strange, and at first sight, I wonder if such a system doesn't beg the question.
If I understand your premise, it goes as follows: given a crypto currency with a coin X, and we want to peg coin X's value to, say the dollar (let us assume for a moment that the dollar is a stable unit of value - which it more or less is in the short term), then if ever market forces push X over $1,- then enough new coins are minted such that its inflationary pressure lowers X back to $1,-. If ever X gets below $1,-, then enough coins are burned so that the scarcity of X makes X back to $1,-.
Your comments seem to point that these new coins, or those burned coins, are distributed according to stake. Let us suppose that at a certain point, Joe has 20 X in his account, and Jack has 30 X in his account. Suppose now that X rises in price, and the amount of X has to triple. In perfect PoS distribution, this means that Joe now has 60 X in his account, and Jack has 90 X in his account. The next day, X crashes on the market, and the number of X has to be divided by 5 and burned to maintain the price. Joe now has 12 X in his account, and Jack has 18 X in his account.
All the time, X is near $1,- but Joe first had $20, then it rose to $60, and then it fell to $12.
In what way is this different from not changing the amount of X at all ?
Suppose that Jack had to pay Joe something that was worth $10. Each time, Jack will have to pay Joe 10 X.
If this happened first, then Joe would end up with 30 X and Jack with 20 X. This would then rise to 90 X resp. 60 X, to fall back to 18 X resp 12 X. If it happened second, Joe would have 70 X and Jack would have 80 X, to fall back to 14 X and 16 X respectively. And if it happened at the end, Joe would have 22 X and Jack 8 X.
So depending on where it happened, at the end of the day, Joe would hold ($18 resp. $14, resp. $22), and Jack would hold ($12 resp $16 resp $8).
Consider now a coin, Y, that is like X, but doesn't do this adjustment. Initially, Joe has 20 Y and Jack has 30 Y. At first, Y is at $1, then it rises to $3, and then it falls to $0.6.
This means that Joe initially had $20, then he had $60 and in the end he had $12 worth in his account: EXACTLY as with X.
Suppose now that Jack has to pay Joe something worth $10. If it happens first, Joe will get 10 Y from Jack, and he will have hence 30 Y and Jack will have 20 Y. At the end of the day, Joe will have then $18, and Jack $12.
If the payment happens second, Jack will have to pay Joe 3.33Y ($10 at $3 per Y). Joe will now hold 23.33Y and Jack will hold 26.66Y. At the end of the day, Joe will have $14 (23.33 Y at $0.6), and Jack will have $16 (26.66 at $0.6). If the payment happened at the end, Jack will have to pay Joe 16.66Y so Joe would hold 36.66 Y and Jack would hold 13.33 Y, so Joe has $22 worth of Y, and Jack, $8.
As we see, the value that people hold is exactly the same for coin X, and coin Y. There's no point in doing this inflation and deflation: a coin that doesn't do it, has exactly the same effect.
What one actually does, with this inflationary game, is simply to change the measurement unit. But there's no stability at all in held sums. If you have an account containing a value of $200, initially, this fluctuates just as much in X than in Y. There's no monetary point in trying to peg the unit.