Bitcoin has the same problem. There is no inherent reason you can't have a cryptocurrency where there is no maximum number of coins to ever be mined and instead the limit is that mining them requires a fixed amount of computation.
That would give you the characteristics you want from a medium of exchange, because there is a rate limit on how much can be created (doing so requires e.g. electricity). Then the value is relatively stable, if you accept it as payment on Monday it would still be worth around the same amount on Friday, but the long-term result is a slow reduction in value on multi-year timescales as compute gets cheaper, so you don't get the speculation that results in high volatility and it doesn't strongly compete with real economic activity for investment resources.
The argument you'll get from goldbugs and whatever is that nobody would want a currency which is inherently inflationary like that, but that's clearly contrary to evidence. Most government currencies are inflationary, even on purpose, and it doesn't matter as long as the rate of inflation isn't so high that people holding it transiently for use as a medium of exchange are losing a significant amount in that short period of time. Especially when the rate of inflation is predictable (the rate at which computers get faster is reasonably consistent) so that anyone entering into a long-term contract denominated in that currency can reasonably predict its future value on the delivery date. Or people could just use it as a medium of exchange and denominate their contracts in something else.
You are right, the harm of unstable currencies is a matter of public perception but boiling the frogs slowly still does harm. Inflation is a significant, longterm, bottom-up wealth pump and simply pointing to empirical evidence is a point against unstable currencies, not for them.
How cryptocurrencies are mined is secondary in that regard too because their values is also purely based on perception, since there is no large authoriry backing that currency by eg. demanding , spending and regulating it.
Bitcoin has the same problem. There is no inherent reason you can't have a cryptocurrency where there is no maximum number of coins to ever be mined and instead the limit is that mining them requires a fixed amount of computation.
That would give you the characteristics you want from a medium of exchange, because there is a rate limit on how much can be created (doing so requires e.g. electricity). Then the value is relatively stable, if you accept it as payment on Monday it would still be worth around the same amount on Friday, but the long-term result is a slow reduction in value on multi-year timescales as compute gets cheaper, so you don't get the speculation that results in high volatility and it doesn't strongly compete with real economic activity for investment resources.
The argument you'll get from goldbugs and whatever is that nobody would want a currency which is inherently inflationary like that, but that's clearly contrary to evidence. Most government currencies are inflationary, even on purpose, and it doesn't matter as long as the rate of inflation isn't so high that people holding it transiently for use as a medium of exchange are losing a significant amount in that short period of time. Especially when the rate of inflation is predictable (the rate at which computers get faster is reasonably consistent) so that anyone entering into a long-term contract denominated in that currency can reasonably predict its future value on the delivery date. Or people could just use it as a medium of exchange and denominate their contracts in something else.