Thinking about proof-of-work-history (POWH) some more.  I think it could make the coin more efficient as well as more secure.

If a branch is characterized by higher scores, it is a more valid branch and not an attacker.  Likewise, if a block within the branch is characterized by a high score (because those mining the block have been mining the coin longer), then you can reduce the difficulty required to accept that block, because those producing the block are more trustworthy.  This reduces the energy needed to secure the coin over time.

Furthermore, stronger protection against 51% attack means that if mining happens to be reduced for whatever reason in the long run, the coin will still be reasonable secure.  That allows long-term energy efficiency with adequate security even for small coins.