There will always be something you can do to reduce power consumption: expecting (or advocating) JS-free versions of all websites for that reason is a completely arbitrary line to draw.
So what could we do today? That is - if we purposefully limited ourselves to just basic HTML, and server-side processing, without any (or minimal) CSS or javascript, and only using the (expanded) tag and attribute HTML we have today?
I don't know for sure - but I believe we could create some amazing things.
Think about it this way: Look at what demoscene people are able to create when they put extremely artificial challenges in front of themselves; we could try to do the same - and see what happens?
Perhaps there needs to be a demoscene-like competition space for this kind of stuff (how much can you get done in under 100k browser-side? 10k? 1k? Limit bandwidth to the backend, too, and maybe server-side size of code?).
Just some random thoughts - it might be something I'd have to try myself, but maybe this post might inspire someone to do it as well...
Recently I was using an expensive mobile connection and I discovered w3m, a text based browser (runs in the terminal). I was amazed at how much faster everything worked.
Most of the sites were still perfectly usable (w3m has pretty good HTML rendering) but some were very difficult to navigate.
My point is, without JS and CSS, the web is just... text.
And when you browse with w3m you realize, that actually the web has always been text. It can be quite refreshing to get all the decorative crap out of the way.
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edit: I now see you didn't say to remove JS, but to challenge yourself to see how much you can make in a tiny amount of JS. Such competitions exist!
web pages https://a-k-apart.com/
java games http://www.java4k.com/
Same thing that is happening with ads and ad blockers.
All ads are intrusive to some degree.
The idea of browsers sending data that the user has explicitly elected to send (in addition to, if we're being pedantic, that the server put there in the first place) is very compelling in this day and age - only problem being that in order for that to have any meaningful impact on web security in the general case, you'd have to more or less universally deprecate JS support, which would set the web in a very different direction indeed.