Are we correctly measuring energy efficiency in proof-of-work?
Yes, here is why:
https://www.truthcoin.info/blog/pow-cheapest/The slower the hash function is, i.e. the more interrupts and memory accesses delays it involves that keeps the processor suspended and maximizes the delays between hashes, the more time and less energy it will consume, and the more energy efficient it will be.
This was proven to be false by a lot of "CPU-based altcoins". For example, if you replace SHA-256 with some slow and inefficient hash function, then you will not only slow down mining, and "kill ASICs". At the same time, you will increase the time needed for Initial Blockchain Download, and the time for verifying anything. Also, CPU-based altcoins moved that to the extreme, where verifying N blocks of the chain was as hard, as mining a new block. Which means, some of those chains died, because it took too long time for full nodes to verify the chain, because it was more profitable to skip verification, to "trust, and don't verify", and just mine on top of the latest block, by blindly assuming, that it was correct.
The idea is not to make the processor work harder between hashes, but to work less, if at all.
This idea is flawed, because if you reduce the work needed for mining, then you increase the work needed for usage. And it is better to have a group of miners, performing a lot of work, while keeping things easy to verify for a regular user, than do the reverse, and make mining easy, because then usage is very painful, when each participant need more work to properly secure their coins, because miners did not put enough effort into that.
The work required to produce a block must scale with the work capacity to maintain the block interval, so it's not about how fast the work is done, but about the time it takes to do it.
It is equivalent in a physical sense, because you can always move any algorithm from "consuming a lot of memory" into "taking a lot of time". And some altcoins also did those mistakes, by assuming, that if something is based on "proof of space and time", then it cannot be optimized with "proof of work". I have bad news: it can be optimized, and it usually is, when people have enough incentive to do that.
Read about Chia or similar altcoins, and learn from their mistakes. Try to use some CPU-based altcoins, and see, how long it takes to verify everything. Basically, you can read about some altcoins, which tried to do, what you proposed, and you can see, what were the consequences.