Why? If OPEX is reduced (lower electricity costs), it's logical to assume that it will be replaced with CAPEX, given how competitive mining operations are. If that's the case, that will mean electricity being used to power ASICs being replaced with chemicals required to fab semiconductors (along with electricity for those fabs). It might be better in terms of GHG emissions, it would be a wash for overall environmental impact.
If you're referring to memory-hard hashing algorithms, I believe those are just resilient to ASICs/GPUs, but still require significant CPU energy. I'm not convinced those would be better for the environment, so if you're referring to those, do you also have an explanation for why they'd draw relatively less power?
They use less power simply because people are going to spend the same total amount of money in terms of compute hardware + energy, however RAM consumes less energy per per dollar spent on it than ASICs/CPU’s etc.
3W per 8GB of DDR4 is a reasonable baseline. https://www.crucial.com/support/articles-faq-memory/how-much...
Did they end up solving the "nothing at stake" problem?
See https://eth.wiki/en/concepts/proof-of-stake-faqs (I can’t link to the paragraph).
The energy usage combined with proof of work is the backing. If you break that for Bitcoin als is left is trust. The energy used and consumed is like the USD tied to gold (which it is no longer since quite some time)