One alternative idea is 'proof of stake'.
And then it always seemed to me, also, that some kind of strategic partial centralisation could help make cryptocurrencies much more efficient..
Honestly, if you are going "big leagues" in cryptocurrency, I don't think having a central authority is bad as long as procedures are in place to contest flawed histories. Peercoin does its PoS through the developers signing key locking history - as long as people trust the devs, they trust the blockchain. If someone can prove the Peercoin blockchain is manipulated, the chain and project can be forked and someone else can be given confidence by whatever measure the community wants to use.
If trust in devs is sufficient, why bother with a blockchain? Just store the history in Git.
Yes, and you could implement that specialisation on top of bitcoin. Just imagine eg one of the bitcoin exchanges that hold your balance for you allowing you to send money to other account holders (even at other exchanges) without that ever hitting the blockchain.
The control to keep that kind of company honest is that people will occasionally demand their balances be paid out in bitcoin.