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."

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.

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.