The profits from Bitcoin mining so far seems to have won out using this mechanism..
0: https://www.sciencedaily.com/releases/2022/01/220119121411.htm
1: https://carbon.xprize.org/prizes/carbonEssentially it's either going to be so cheap that trying to use it as currency is impractical, like carrying around pennies, or so overvalued that you'd surely destroy the economy? You'd have to use paper currency backed by tonnes of carbon - which is just a roundabout way to arrive at carbon credits!