but the two chars saved are not worth mentioning, are they?
Many people consider the URL without the hash considerably more "pretty" or "user friendly". Also, a very big difference is when you browse to a URL with a hash (a "fragment"), the browser does NOT include the fragment in it's request to the server, which means the server has a lot less information available to deliver the right content immediately. As compared to a regular URL without any fragment, where the full path "/home" IS including in the HTTP GET request to the server, thus the server has the option of rendering the actual "/home" content directly instead of sending the generic "index.html" content and waiting for javascript on the browser to update it once it loads and sees the fragment is "#home".
HTML5 mode is also better suited for search engine optimization without any crazy escaped fragment hacks. My guess is this is probably the largest contributing factor to the push for HTML5 mode.
How is this related to HTML5?
HTML5 introduced the necessary javascript APIs to change the browser's location bar URL without reloading the page and without just using the fragment portion of the URL. Here's a demo
It seems like the purpose of this rewriting to make the server return always the same page, no matter what the URL looks like. But doesn't it read to needlessly increased traffic?
Nope, it's the opposite. The server ONLY gets a full page request when the user first clicks a link onto the site OR does a manual browser reload. Otherwise, the user can navigate around the app clicking like mad and in some cases the server will see ZERO traffic from that. More commonly, each click will make at least one AJAX request to an API to get JSON data, but overall the approach serves to reduce browser<->server traffic. If you see an app responding instantly to clicks and the URL is changing, you have HTML5 to thank for that, as compared to a traditional app, where every click includes a certain minimum latency, a flicker as the full page reloads, input forms losing focus, etc.
It works neither in my Chromium 25 nor in my Firefox 20. Sure, they're both ancient, but everything else I needed works in both of them.
A good implementation will use HTML5 when available and fall back to fragments otherwise, but work fine in any browser. But in any case, the web is a moving target. At one point, everything was full page loads. Then there was AJAX and single page apps with fragments. Now HTML5 can do single page apps with fragmentless URLs. These are not overwhelmingly different approaches.
My feeling from this back and forth is like you want someone to declare for you one of these is canonically more appropriate than the other, and it's just not like that. It depends on the app, the users, their devices, etc. Twitter was all about fragments for a good long while and then they realized their mobile users were seeing too much latency and "time to first tweet" was too long, so they went back to server-side rendering of HTML with real data in it.
To your other point about rendering on the server being "a lot of work", it's true but some consider it the "holy grail" of web app development. Look at what airbnb has done with their
rendr framework. See also Derby JS. My point being, if you decide you want rendering in both the browser and the server, you pick a framework that offers that. Not that you have a lot of options to choose from at the moment, granted, but I wouldn't advise hacking together your own.