It's all a matter of control, in my opinion. I'd say that iOS is practically an everything app, but Android is not. ChromeOS may be borderline, because of the hoops one has to jump through to side-load apps.

As originally defined, an OS is a set of functionalities offered to user-programs for accessing hardware, memory and similar things at a higher level - in it's original intent, an OS was passive. A browser originally also had the intent of being just a receiver/displayer of the information the user requested. Of course, browsers have indeed become more likes OSes as web pages have become like programs.

Of course, mobile OSes and OSes in general have become active and oriented to filtering input as well as generating inputs. This creep is everywhere - MS Windows displaying adds and flogging it's "app store" is one notably noxious example.

Philosophically, an OS is a virtual computer meant to be shared among programs (usually an open-ended set of programs, and usually regulating how they interact). You could say the web is not that because it's a distributed system instead of a virtual computer, so the browser makes a better match.

I guess an everything app would be different in that its maker probably goes like "Open-ended set of programs? Who cares, you nerd, I'm just gonna make deals."

Chrome has a similar market share on mobile as well, especially since it's the built-in browser for Android

If anything the mobile browser situation is much worse.

On one major platform, there is Chrome by default (so even bigger market share issues). People can install other browsers, but far fewer do than even on desktop. For those that do, most use the Play Store which has some conflict of interest concerns.

On the other platform it's even worse. The only option is Safari and the conflict of interest is fully realized because other browsers aren't even allowed on the App Store

The relevant difference is that a single entity doesn't control all the functionality and layers.