As for whether "shaving a couple of bytes off of a header" makes a practical difference, you should consider the "Why do we need header compression?" answer here: http://http2.github.io/faq/ which references concrete evidence provided by an HTTP2 advocate. Personally, I find that more convincing than your apparently unsupported assertion.
Separately, it's nice to say websites should drop the eye candy and the Javascript frameworks (the hundreds of requests is addressed by HTTP2 multiplexing, I believe), but that's missing the point. As has been repeatedly demonstrated since the earliest days of WAP, mobile users don't want a stripped-down subset of the Internet, they want as much as they can get. From that perspective, raising the bar on what's possible (as HTTP2 tries to do) moves the ball far more than trying to convince websites to fit themselves into today's constraints (especially since the mobile user in the developing world has one of the strictest versions of those constraints).