No, I think once ethereum goes PoS, average people will stop caring about the energy use of crypto because the public at large won’t be able to digest the nuance.
The average person with a computer in the US (just taking the country I live in) has never heard the words “proof of stake” or Ethereum.
All the average person knows is that there were a bunch of Super Bowl commercials about “crypto”, and their cousin who spends a lot of time on the computer lost a lot of his parents money investing in a thing called “Bitcoin” last year.
You can bridge bitcoin natively to Avalanche (look up btc.b) and then you can trade bitcoin with low fees, fast finality, get smart contracts, use it in defi.... oh, and it's proof of stake already so more environmental.
Just saying :)
that just makes the environmental asterisk bigger. you buy bitcoin you wouldn’t have bought otherwise (or would have sold otherwise), bridge it, lock it up on a different network. these actions marginally push the price of bitcoin up. higher price means (temporarily) more profitable mining, means miners divert more power to mining.
the existence of ethereum as proof-of-stake makes it impossible to stop proof-of-work coins via exchange regulation/etc. It's trivial to run exchanges on ethereum and therefore they largely exist outside any possibility of regulation. Previously you could sorta leverage this in via the exchanges/etc but now there is no possibility of ever banning the environmentally-harmful PoW coins.
Your post makes many assumptions. One - existence of trustless bridges from PoW chain to Ethereum (trustful bridges are rather easy to kill). Second, regulation can be achieved in a way OFAC does it - "anyone who holds/buys this token is a felon". This drives money away from the chain, reducing its PoW budget.
And I really suspect that Ethereum will win the race anyway. At least until something really juicy appears (like private contracts, chain-managed secrets, etc).
But, at least to me, this will make ethereum-based NFTs of interesting art a more morally-justifiable purchase.