I also see no purpose of competing with CBDCs or how this your proposition could actually rival them. CBDCs are government backed and designed to serve as an alternative to the native fiat, creating a protocol does not compete with that.
Bitcoins heavy reliance on layer 2's blurs the line of true decentralized exchange at high volumes. How the bitcoin protocol is currently setup it is best designed as a long term-value store(in my opinion).
It is not necessarily the goal to rival CBDC's in all aspects but to provide an alternative medium of decentralized high traffic value exchange(lower value higher volume). The aspect of CBDC's that is being competed with is the function as a daily digital spending currency in the digital space. In a virtual world unbounded by physical borders using a country backed token ensures little to no privacy. The goal is to provide a truly decentralized option for high transactional volume network demands. Both POW and POS have their own limitations and the only way to find out if a new approach could work is to try it. I understand it is difficult to predict how the network will function at scale being the reason I wish to distribute the majority of the initial supply at no cost.