Few websites use them effectively yet, at least in a way that benefits the consumer (several are using them to benefit marketers). This could be because developers don't know about them, consumers don't care about them, or perhaps just not enough time has passed. XHR was introduced in 1999, after all, but it took until 2004 before anyone besides Microsoft noticed it.
I think many of us underestimate what was possible to do in browsers. What has happened is that these features have been democratised: what took them months to build I can now pull of using WebRTC in the space of a weekend.
The thing is - the polish matters. You can't do viable consumer apps until they actually work like the consumer wants, which is often decades after the technology preview. You could emulate websockets using IFRAMES, script tags, and long-polling back in the late 90s, but a.) you'd get cut off with the slightest network glitch and b.) you'd spend so much time setting up your transport layer that you go bankrupt before writing the app.
They're taken for granted in native application programming, yes, but the big advantage of browsers is the zero-cost, on-demand install. This is a bit less of an advantage than it was in 2003 (where new Windows & Flash security vulnerabilities were discovered almost every day, and nobody dared install software less their computer be pwned), but there are still many applications where getting a user to install an app is a non-starter.
Ditto. I like having a copy of a program that no one but me has access to modify, and I like that I don't have to rely on my ISP to use my computer. If I like a program, I don't want it to change until I choose to change it. I don't want to be A/B tested, marketed to, etc. I'd rather buy a license and be happy =)
Everything else seems like stuff that makes things better for the developers but not much visible benefit to the user. I can understand where a comment about the web not being much better would come from, on the scale of a decade.
Go back 20 years, and you're talking about a completely different world; frames, forms, webrings, and "Best viewed with IE 4.0". But if '96 to '06 was a series of monumental leaps, '06 to '16 looks like some tentative hops.