I think I should have been clearer that I wasn't talking about power efficiency in that response, I was talking about time efficiency, in the sense of how long it takes to run the algorithm or, in the more usual term, your rig hash rate.

Then, restating what I said, if you could devise an algorithm to solve PoW in a fraction of the time, it would counterintuitively disrupt and collapse the chain. Only minor improvements to time efficiency are OK. Significant strides are not.

Getting back to the power efficiency issue that you brought up again, the best way people found so far to avoid the power hunger of PoW is not a better PoW but a better proof system, such as proof of stake (PoS). The reasoning is "why fix a broken system if you can make a better one?"

I get your point about how gasoline cars need to be phased away, not abruptly removed. That's not the case for digital systems such as bitcoin. The world doesn't need BTC or would die without it. Money would just flow elsewhere. The only reason BTC is still there and has all that money invested is simply because people believe in it or are gambling to see if it grows more. The comparison with gasoline cars doesn't hold here.

But hey, I was the one that brought gasoline cars on the first place, right? That was me doing a poor analogy. Which I made sure to mention it was a poor analogy on the first place.

I mentioned it as an example of how some systems should be replaced, not improved, which is the case of PoW or gasoline cars. The major difference is just that cars are a physical thing and, hence, are a lot harder to go away and, hence, need to be phased out as you said. PoW is digital, it can go away much faster.

Finally, about your comment on writing PoW algorithms that actually spend work doing something useful. That's a nice idea and is what I believe some people are trying to do with CHIA and other alternative proof systems. I am not aware of one based on PoW though. If I am to guess why, the main problem is that for an algorithm to be PoW-usable, it needs to be very hard to solve, have some form of controllable difficulty and, at the same time, have its solutions be verifiable in trivial time. This last part is what makes some of the "hard but useful problems" unusuable for PoW.