I agree there's different solution for different consumers. This particular branch of the discussion is just on whether streaming is greener than console gaming. Consideration 1 is whether steaming uses more energy or not. Consideration 2 is whether that energy is greener than that powering home consoles.
It's an interesting discussion and I don't think we're equipped here (not enough actual numbers) to determine which would actually be greener.
But some other things to consider (in addition to some things you touched upon).
A console purpose build for stream should consume less energy than a console built for traditional play. Does this offset the increase power usage of a server farm?
A console purpose built for streaming is also likely to feature much less in the way of hardware resources (part of the energy savings as well as cost savings). It likely won't need a mechanical HDD, optical drive, or high powered SOC, saving both on costs and energy on those fronts. Which means it'll also require less exotic cooling and a smaller and probably cheaper PSU. If one could make it passively cooled, that further reduces the energy footprint and build costs. But do the savings on millions or tens of millions of units of consumer hardware balance out the costs of increased server infrastructure and server maintenance?
Being smaller and cheaper to build, likely means it's not just smaller, but likely lighter. This means shipping costs should be greatly reduced. Ship multiple streaming consoles in the same space as a single traditional console. But again, there's also the costs associated with all of the streaming infrastructure (machines, cooling, power transformers, etc.)
Being smaller also means less material resources are consumed for the manufacturing of each console (good for the environment and the wallet). OTOH, there's increased material usage for building out the server farms.
And finally, something touched upon by Brit. Large corporations are increasingly looking at alternative energy sources that can be located on site (solar power, for instance) to power server farms. That may go a fair ways in reducing the energy consumption incurred by those server farms.
I have no answer, but it's interesting to think about.
That said, I have yet to use a streaming service that I would consider to be adequate (not even pleasant, but just adequate) for any action oriented game. Both graphically and related to that, in game feedback to player input.
Regards,
SB