Preventing double spending is the reason for all of this hullaballoo, no more, no less. It's easy to create a distributed ledger, but hard to create one where you cannot double spend, hence mining and staking.
You can't double spend physical cash because you can't give someone else a physical object and have it too.
You can't double spend your fiat because your bank says to your counterparty "trust us bro, he didn't double spend" and your bank is pretty trustworthy.
You can't double spend your bitcoin because to do so you'd have to have more than half of the computing power in the world, which is pretty tough to do, and even if you did actually succeed at double spending it would render your investment worthless, because all transactions are public and someone might notice the double spend and the value of bitcoin would plummet.
Soon, you won't be able to double spend your Ethereum because if you did, everyone would notice, point it out to everyone in the network that you double spent, and then everyone would automatically slash your Ethereum stake to zero going forward and carry on without you.
That's all. It has nothing fundamentally to do with voting or economic distribution or proving ownership of scare resources or anything like that. It's about preventing double spending on a distributed ledger of transactions.
If you solve double spending, then yes, your cryptocurrency will work.
(reposting this from the github)