The energy saving comes from the fact that most of miners will spend a big part of their time on Round 1 that is not heavy-energy / CPU consuming. At least this is the target, the bet and the hope.
I'm afraid exactly that you might be right, and you might succeed
The newly mined coins plus the transaction fees for the transactions included in the block have a certain value.
So it is obvious that the market will seek equilibrium and to channel the resources needed to mine with a similar market value (I assume that mining is still to be permissionless, and we will not create a miners clique or cabal where market law does not apply).
The precedents are not really optimistic...
Memory intensive mining algorithm like Scrypt can effectively reduce the energy intensity of computation. But then the mining equipment itself becomes the main investment of the miner, and the benefit to the environment is disputable due to increased e-waste production.