However, if the iPhone came out in 1997 when websites were mostly static html pages, provided the browser could wrap text, it would be an excellent experience. An iPhone's screen is about the size of a few paragraphs from a newspaper column; it's not tiny, in fact its perfectly sized for ergonomic reading. The most praised reading apps on mobile these days are just a plain background and a block of text consuming the whole screen, with the rest of the ui getting out of your way.
I think that you are 100% incorrect: the Web (i.e., HTML) is perfect for small devices with touchscreens. As asdff notes, late-90s websites would work perfectly on a mobile device. It's all the cruft we have spent the past twenty years polluting the Web and our browsers with that doesn't work so well in a mobile context.
A mobile phone is perfectly capable of displaying images and text. HTML is perfectly capable of displaying images and text in a device-independent fashion: that was its raison d'etre, as I recall.
I think where we went wrong was assuming that browser windows would be maximised on a desktop screen. That, and JavaScript.
The idea is not to disable ability to run browser and millions of website will continue to exist, but Top 1000 web properties and 99.9% of traffic and money will move out.
In current scenario, you can still run a BBS and share some really interesting content, but it will be a niche of nerds and fanatics.
I'm in favor of retiring the web. Not that it will happen any time soon. How many reasons do we need? Private information leakage alone should not be tolerated. Accessibility? Attack surface? Resource efficiency?
Obviously I'm missing the point, because none of this explains why internet is what it is. I sure wish it were simpler.
However, the main reason these apps gained all this traction is that the Web is simply not made for small devices with touchscreens. It's the discomfort of using web browsers on mobile that created the tipping incentive to adopt these streamlined apps. As long as people keep using more comfortable devices (eg. laptops) that can easily browse the Web, this segment will not have that "discomfort" incentive to move away from the Web and onto more restricted platforms.
Yes, there could be other incentives - you mention junk sites and security issues - but these aren't strong enough to outweigh the main advantage of browsers, which is the breadth and momentum of the Web, something that users still value. I hope I'm right.