This has been one of the most frequently brought up topics for Bitcoin and people have tried all kinds of other things instead of the original algorithm.
And at this point I don't think any alternative will win just because they came up with a "more efficient" algorithm. PoS may have a chance (although personally I'm skeptical) but something as drastically different as PoS may only have a chance against the Bitcoin's algorithm.
The usual response to this inefficiency argument is "securing the ledger itself is a very costly job. It's basically trying to replace all the bank/credit card networks and when you consider how much energy goes into an aggregate of maintaining all of them, Bitcoin PoW is nothing".
But aside from that, I think sometimes inefficiency IS the feature, for example double entry bookkeeping is inefficient because it's redundant, but it revolutionized modern accounting.
There are a number of distributed computing projects (e.g. SETI@home): https://en.wikipedia.org/wiki/List_of_distributed_computing_...
The Ethereum White Paper lists a number of applications for blockchains: https://github.com/ethereum/wiki/wiki/White-Paper
(BitCoin is built on SHA-256, Ethereum is built on Keccak-256 (~SHA-3))
Proof-of-Stake is a lower energy alternative to Proof-of-Work with tradeoffs: https://github.com/ethereum/wiki/wiki/Proof-of-Stake-FAQ
Unfortunately, IDK of another way to find secure consensus (blockchains are consensus protocols) in a DDOS-resistant way with unsolved problems?
Gridcoin (Berkeley 2013) is built on Proof-of-Stake and Proof-of-Research. Gridcoin is used as payment for computing resources contributed to BOINC.
I doubt that volatility would be welcome on the Gridcoin blockchain: Wikipedia lists "Supply growth 6.5% Inflation. 1.5% Interest + 5% Research Payments APR" under the Supply Growth infobox attribute.