The replacer inherently CAN'T have the same pricing stability as the currency it is replacing. [/u] The former has to rise against the latter which includes against items priced in the latter.
Of course not. In Europe, many currencies were replaced by the Euro, and the Euro didn't "rise" against these currencies to replace them. The Euro got more and more participants, and replaced bigger and bigger markets, as new countries adopted the Euro, but the Euro didn't "rise" against these other currencies.
Imagine that an imaginary bitcoin was emitted at against, say, $1 in the beginning, and that it had an emission scheme to keep it around $1. (my proposal is to have proof of work that is about $1 worth, and can do as much proof of work as you want and emit as many coins as you want with that: if you are willing to burn about a million $ worth in proof of work, you own now a million coins ; if you want to burn a billion $ worth of PoW, you now own a billion coins). Suppose that people like it, and start using it more and more. Slowly, it starts to replace payments about everywhere. The extra demand for the currency, to be able to use it (Fisher's formula) would make it rise in value, but that makes it more interesting to mine it, and it costs about the value of $1 to mine it, so people will mine a lot of it until it lowers again to near $1 value. If it is less than $1 in value, nobody will spend PoW on it to make more of them, and none get emitted. But if more people use them, more and more coins are in circulation. The monetary mass, the market cap rise, and they replace soon most payments. But nobody can get rich with it. It is a currency. Its value is stable (the value of about $1 of proof of work). You can write a contract in it. You know its value will remain stable (at least, will not deflate like crazy and become a rare collector's item).
Comparing fiat to crypto is apples to oranges. Replacing one fiat with another is not the same thing as replacing fiat with a non-government currency. I think you are arguing details and failing to see the point.
Your emission scheme is just that - a scheme. Why would you want to peg to something you want to replace? That doesn't make sense. My guess is you're an older fellow who just can't wrap your head around life without the USD.
It takes years of brainwashing, like majoring in Economics-style-brainwashing, to think deflationary currencies are bad and elastic money supplies are good. Its the foolishness, if not downright insanity, of thinking that there is a magic algo or philosopher kings who can decide what the volume and value of money should be on any given day rather than leaving it to the market.