What? The size of a page has nothing to do with the CPU. Most of that size is going to be in images and animation, and most web pages put basically no load on your CPU. If one does it's going to be because of badly written JS, not because of the size.
Shrinking the average page size even by half is not going to "the web run faster on a large scale." Most of the time your page load speed is not affected by congestion, and if it is it's likely due to a local tower or something. The problem there will be the number of users per tower, not the size of the pages they are loading.
Parsing text can be hardly parallelized. Overall it will increase the price of your phone so it can show that webpage fast enough, which will be a cost of both CPU and battery. I have a shitty bi core smartphone, and it really doesn't like webpages. When you look at the source of a page, there is no justification for all of this, unless you like complexity.
I did not want to talk about HTML on smartphones, since it already seems to be non existent since apps replaced HTML, but do you really think we should have apps instead of webpages? Apps are less open. I really think HTML parsing is power intensive, and that you could actually increase autonomy and speed on HTML, instead of just having bigger batteries. Seems to be the same argument than fuel efficiency regulations.
Maybe I say all this because I like minimalism, but at the end of the day, most core formats are designed with acceptable performance in mind. In my opinion, HTML doesn't have acceptable performance.
Are you sure that parsing HTML is the step that is the biggest issue for your phone, and not e.g. rendering or JS execution? (It's certainly possible, parsing HTML with bad parsers or pathological content can take surprisingly long, but it's generally the last thing I'd expect as a reason for a browser to be slow)
I linked a computerphile video explaining how HTML ended up as a loose defined language, meaning browsers will often struggle to render something.
I think it's part of the whole thing, HTML is too permissive, and it also will make rendering slower. If HTML was better defined from the ground up, rendering would also be faster. The sites I visited were not really JS intensive. JS is also a problem for webpages.
Anyway I hate HTML/CSS/JS in general for all those reasons. Parsing text is already painful, why do it each time you visit a webpage?
Shrinking the average page size even by half is not going to "the web run faster on a large scale." Most of the time your page load speed is not affected by congestion, and if it is it's likely due to a local tower or something. The problem there will be the number of users per tower, not the size of the pages they are loading.