There are some great native apps out there and a lot of them do things you couldn't do on the web, but nowhere near close seems like a stretch to me. There are some great web apps out there. And while there are great native apps made with love there are also perfunctory, rushed, clunky ones that could have just been a website.

People often overlook some of the functional UX the web brings to the table. For example: on the web I get consistent search and text highlighting behavior, consistent notifications, consistent navigation behavior (back buttons, history), I can tab to focus (usually), and I can use plugins to customize the content. Even the idea that you can reset the application state with a refresh is something I wish I had on some native apps.

Can you give some examples, please? I can't think of a single thing that cannot be overcome by good design.

They never look and feel exactly like native apps, even the ones that try a bit.

Some widget will be rendered wrong, they'll use the wrong font (or even hinting!), right click may not work as expected, they won't use multiple windows correctly, etc.

Even React Native gets some of this wrong, although few use that on desktop.

If you're a user that appreciates consistency on your OS, all of this will stick out and annoy you. And you'll end up using Apple's Mail.app over GMail's UI.