That's a good point. The net is great for shoving data backwards and forwards but for the web it doesn't necessarily mean that the browser should be expected to do EVERYTHING.
There used to be a time when most of the posts here on HN were "something native IMPLEMENTED IN JavaScript in a BROWSER" but thankfully those times have passed to the most part.
The Internet was heralded as solving cross-platform problems (hurray for XML?) but it seems that writing a native app actually involves less testing. You now have to test in 3 or 4 browsers per platform, not including mobile devices and changes between different versions. The relentless shoving of features into browsers is no different to what they've been doing for years but I can see why people would not enjoy it, particularly with the repeat of "only works in IE" that you see ("only works in Chrome").
imo the browser is just a better navigation model for a wide range of apps than typical OS GUI shells. so it's natural that either native apps get hosted in the browser (the plugin model) which has gone out of fashion, or APIs to do whatever an native app wants to do get added to the standard web API.
We've apparently decided that we should use "the web" for everything, whether or not it's a good fit. So yeah, browsers are unavoidably going to accumulate features that used to be the responsibility of apps or the OS. And there will be lots of browser-specific functionality unless you're willing to wait 5 years for W3C or WHATWG or whoever to finalize a standard.