Genuine question - What about a "cashless" currency based on blockchain? (a la bitcoin). Wouldn't it be and not be under any single entity's control at the same time?
- The current biggest problem that bitcoin faces is one of scale - and there's no clear solution in sight. Why on earth would you want every little transaction on the blockchain? If I buy a stick of gum, that doesn't need to be on public record for eternity. It is impractical and unwieldy.
- Centralized systems are always more efficient than decentralized ones, and systems naturally tend toward centralization. Bitcoin falls down under centralization, which we are also currently witnessing with the hash power tied up by a few largely unknown Chinese operators.
There are proposed solutions like pseudo-centralization with LN where bitcoin just becomes a settlement layer for off-chain contracts - and the details behind LN are still so primitive it is not clear it will actually solve any real problems.
What you are talking about in practice for something at scale is a centralized blockchain of some sort, which is really just a distributed, immutable database, with some sort of trusted signing authority. What exact advantage does that give aside from potentially non-reversible transactions, which are a clear non-starter for most consumer purchases? There are already services that offer true non-reversibility for special cases where this is desired.
There has so far been no viable application for blockchain technology as a replacement for cash except black/grey market purchases.