I think we are having the opposite problem: native apps are really starting to look and feel like web apps, and in many cases, they are.
The problem: the web has a terrible UI toolkit for desktop apps. It has clickable links and basic forms, that's all. It was made for documents, not apps. If you want better than that, you have to rewrite it all by yourself, or more likely, import a framework that does it for you. Traditional Windows apps all use system provided common controls, because they are good, and therefore they have a consistent look and feel, even through OS updates. It is even user customizable. Now it is not uncommon to see 10 different styles in a single screen, Windows since 8 is not even consistent with itself, and it is becoming worse every version. And it is not just aesthetics, there are serious usability concerns here, and system-wide customization is gone.