OK, let’s approach this from another angle.
The core problem Bitcoin tries to solve is how to get consensus in a continuously changing, free-for-all group. It “solves” this essentially insoluble problem by making everyone walk through treacle, so it’s always evident who is in front.
But the problem is, it isn’t really evident. Slowing everyone down doesn’t take away the core problem: that someone with more resources than you can eat your lunch. Right now, with only modest resources, I could rewrite all of Bitcoin history. By the rules of the game, you’d have to accept my longer chain and just swallow the fact you thought you’d minted money.
If you want to avoid that, then you have to have some other route to achieve a consensus view of history. Once you have a way to achieve such a consensus, then you could mint coins by just sequentially numbering them instead of burning CPU on slowing yourself down, using the same consensus mechanism.
Now, I don’t claim to have a robust way to achieve consensus; any route seems to open to attacks by people with more resources. But I make this observation: as several people have noted, currencies are founded on trust: trust that others will honour the currency. It seems to me that there must be some way to leverage this trust into a mechanism for consensus.
Right now, for example, in the UK, I can only spend GBP. At any one time, in a privacy preserving way, it would in theory be possible to know who was in the UK and therefore formed part of the consensus group for the GBP. We could then base consensus on current wielders of private keys known to be in the UK, the vast majority of whom would be honest. Or their devices would be honest on their behalf, to be precise. Once we have such a consensus group, we can issue coins simply by agreeing that they are issued. No CPU burning required.