Forget using POW to secure a ledger. It's comically bad because of the wasteful arms race which now makes each transaction take as much energy as a household does in a day(!)
The reason bitcoin is so far ahead is because it was the first. Proof of work to secure the blockchain AND also elect a dictator to mine the next block is cute, but I wish they had decoupled it, as they did for example for bitcoin-ng.
What I am far, far more interested in is proof of work for avoiding sybil attacks, or used COLLABORATIVELY by nodes to secure a history, as done in Ripple for example.
So, back to sybil attacks: proof of work, can we trust it?
What are the best ways to make it expensive for an attacker to create multiple identities, yet cheap for everyone else to make one identity?
One is the cumulative time and activity invested by you and those who invited you.
For example, reputation. Maybe making accounts is cheap but reputation comes from random nodes with reputation upvoting you. But then you can spam all those nodes since they're operated by humans.
It seems we have yet to design a system that's truly impervious to sybil attacks. The best we have is tying things to a human real world transaction, eg buying a smart phone, and hoping that whoever made the smart phone also has a service to sign data (they don't) that wasn't compromised.
Any other ideas? Paying for accounts with bitcoins? That at its root is just back to the proof of work arms race and reputation of bitcoin.
Question: is there some sort of service by the Secure Enclave that can sign a piece of data with an HMAC or something to prove that it was signed on a legitimate, non-jailbroken smart device?