I find it hard to imagine a scenario where this technology pays off. Any examples of real live systems that gained from this?
Repeated experiments - by Google, Amazon, and many smaller websites - have shown that lower latency directly translates to higher conversion rates, so I wouldn't be surprised if this results in billions of dollars of extra commerce, and even a small website would get noticeably higher revenue if they did this. Google also ranks faster websites higher, and so you get an SEO benefit as well.
It's a little inaccurate because Google Search uses chunked encoding, and so it sends the header immediately, even before the search has finished, then blocks as the search request comes back. Plus there are usually inline images at the end of the response, but I chose my query to avoid them. It should still be pretty close to the general ballpark.
* Being able to embed comments which aren't visible to the world is very useful.
* Being able to remove non-important whitespace removes clues on the complexity of generation (though it's a super-complex thing to actually remove only the non-important whitespace thanks to <pre> and CSS styling).
* Linting is another area where things are interesting too. Validators might tell you if your HTML is well structured per the specs, but my js skills and habits have improved as a result of linting. The process might tell you that it's best practice to use readonly instead of readonly="readonly" on an element or similar. Sure, not directly related to minification, but the parsing needs to be done already.
* Minification adds some security through obscurity by making stuff like XSS attacks slightly more difficult (if you use name/id/class mangling). I've only seen this in practice on gmail (most gmail browser addons/scripts break every couple of months when google changes something that alters the generated button ids)
I haven't seen minification done on raw HTML, but have seen non-html solutions used in order to be able to include comments - this is a bit dumb to me.
I've used HTML preprocessors to concatenate separate (single page app) html resources (templates) for delivery, so the pipeline's already there.
EDIT: Especially in mobile/touch-only browsers who are extremely unlikely to inspect the code. So do it for m.example.com, I reckon.
I myself have gotten a little lazy, because I'm hosting my static websites behind CloudFlare who do minification anyway, so I haven't thought much of this in a while.
It adds complexity to your setup and server side load. I would not call that barely anything.
But you can minify your HTML at least.