GP's critique is not that web browsers render SVG and PDF in addition to HTML. It's the outsized role of JavaScript specifically: our browsers execute arbitrary (possibly user-hostile) code while simultaneously trying to protect us from its effects.
That mechanism doesn't necessarily need to involve code being delivered directly from the same server the document is coming from, mind you. It could instead involve an out-of-band app store, where accessing a URL zero-installs a heavily-sandboxed plugin required to view it, and loads it into the browser. (Implementations of this: iOS App Clips; Sandstorm grains.) But those apps are usually still created by the same developer as the document anyway, so there's little difference between this out-of-band zero-install app approach, and having Turing-complete web documents. Either way, the developer of Boogle Maps can still mine bitcoin in the background while you have the map loaded.
It’s also a side effect of the demands of the attention economy fighting against Apple’s refusal to allow web notifications on iOS.
Basically, I don't see consistent patterns of good or bad between web and native apps to justify your comment that "apps are better at being apps than a web browser".
Most GUI apps, native or otherwise, get associated with a brand. Especially the good ones. I'd buy Ableton swag, I love the brand that much.
The VAST bulk of web apps are NOT browser version specific. It's largely only bespoke, internal corporate apps that are tied to one version of a browser.
The B2B productivity/collaboration app space — where you can expect that all your users are mainly using full PCs — is firmly all-in on in-browser web-apps, with their mobile experiences being second-class afterthoughts.