How was it, Proof of Validation, Proof of Advanced Delegation, so Proof of Destruction now?
1. Focus all mining work on the same block by getting all miners to work for the same pool, or create a super pool that consolidates the work of all mining pools. This would distribute block rewards most fairly but it would reduce energy consumption the least as the minimum work required for a share of the block rewards would only discourage the slowest miners from participating. This can be adjusted though.
No, it won't as the same amount of reward is distributed based on the corresponding hashes created, nobody will turn off their miners because it will mean they are losing money. Miners burn energy because for each spent cent for that they get x cents in return, if suddenly for 1 cent they would get 1 $ everyone would be plugging more and more miners, not dropping out.
And I don't understand what slow miners are and not why they would be discouraged.
2. Employ some kind of dice roll or rock-paper-scissor scheme to select a miner at random who then does the actual work alone. This would greatly reduce energy consumption but it would not distribute block rewards as fairly as solution #1. Hash power would no longer effect a miner's odds of winning so this would eliminate mining pools.
It will simply mean miners will create a lot of solo workers for each miner and a lot of people will plug in a ton of USB sticks, mining will stop becoming profitable for large miners, you're going to see a drop in hashrate, and with all the discarded gear sold at scrap metal price anybody with a few bucks could launch a 51% attacks on the network.
3. Yet another idea is to have nodes announce their intent to mine (register) and wait their turn in a queue.
This is not even PoS as jackg said, it's worse than it, making ques for it it's one of the weirdest ideas I've seen, it would be so centralized you could drop the whole confirmation and blocks thing, just rebrand it as visa 2.0.
Moore's law and the doubling of transistors on a given die size, will improve mining efficiency, as long as it remains a relative constant.
Efficiency doesn't mean lower consumption, if BTC goes to 100k you will see people spending more money on gear as those are more profitable ending with more gear and more consumption despite being more efficient.
You will simply get more hashrate for the same $ but the running costs out of which the biggest chunk is electricity is tied to the daily reward.
