In the meantime here's my revised thoughts about volatility.
Even Hayek Money, the best money ever devised, is powerless at eradicating the volatility of the value of money: volatility is an intrinsic property of demand dynamics. The variation of demand over time cannot be artificially governed: nobody can alter this matter of fact and oppose the resulting change in value. Rebasing the monetary stock supply can absorb the volatility impact of variable demand, steering its instability effect away from prices and toward wallet amounts instead. The relevance of such elastic supply of money should not be underestimated, as it will trigger a virtuous loop for volatility too: as long as the currency keeps constant value, a sudden large variation of its demand will become unlikely. Moreover, the availability of stable prices will surely help the growth of the economy using that given money, providing a further benefit in terms of a reduction of the demand/supply variability. In the case of cryptocurrencies the noise due to the variable adoption rate and the need to resort to fiat currencies will be progressively reduced. The only remaining volatility contribution would then just be the variability of the cryptocurrency adoption rate, and this is exactly what is sterilized by Hayek Money through elastic supply of money.
How is it that Hayek money does not have stable purchasing power? If the unit is pegged on a basket of goods, eg, and changes in the demand for the unit causes a rebasement, such that it still purchases the same goods, then there is no change in purchasing power?