Proof-of-work is already incredibly energy-friendly. The network has no energy minimum requirement, it simply runs on whatever excess power the miners are willing to spend on mining. Thus energy use is self regulating.
This is true if you measure energy efficiency against the mining rewards. A miner usually seeks to reduce his power consumption in order to increase his net profit. However, if you look at how much security you can get out of the total mining power, Bitcoin's PoW model is far from optimal.
Let me explain why. Bitcoin mining is a continuous process whose security is determined by the hash rate available at any given time. Therefore, an attacker only needs to accumulate 51 % of the
current hashing power for a short time (i.e. by renting the hardware) to launch a successful short-range attack, i.e. to replace the most recent blocks of the chain by his own arbitrary blocks (with a double-spend).
On the other hand, to change the whole history of the network, potentially as far back as the genesis block, the attacker would have to generate an alternate chain faster than the existing chain. Such a long-range attack is extremely difficult to achieve because one would have to outpace the hashing power of all the honest nodes for a very long time. Hence, the Bitcoin network provides a much higher level of security against long-range attacks than with regard to short-range attacks. In other words, the mining power materialized in the existing blockchain (i.e. the total mining energy used thus far) only backs the existing chain but not the creation of new blocks. The mining energy is wasted in that regard, which is sub-optimal.
To overcome this issue, we could use a separate blockchain (meta chain) to determine the block creation order of the actual transaction chain. This could be done by selecting a random block of the meta chain whose creator is elected as the miner of the next block of the transaction chain (Of course, this requires a selection process that is truly random and manipulation-proof). In contrast to mining the meta chain, building a block of the transaction chain will come with a reward for the creator.
The security of the transaction chain does not rely on the network's current hash rate but on the
cumulative hash power stored in the meta chain. With such a model, short-range attacks would become equally hard as long-range attacks.
Contrary to what one might think at first, this system does not facilitate centralization any more than Bitcoin's PoW already does. As mining is a dynamic process with miners coming and going, one would have to exhibit the same relative mining power during the whole lifetime of the currency in order to preserve the same share of the mining rewards.