How is a web browser not an essential part of a desktop OS.
Literally every single consumer operating system comes bundled with a web browser, and in fact everyone bundles their own
OSX: Safari
ChromeOS: Chrome
Windows: Edge
That's so 1997. I would argue that a desktop OS isn't essential to my web browser. All I want my phone or my desktop computer for is to browse the web (not me but that's true for the vast majority of people). All this nonsense that comes with the OS is peripheral. Not essential. The only thing my phone or desktop needs to do is turn on, connect to the web, and download facebook.com and any other website I want. That's it. That's essential. Network card: essential. Web browser: essential. Any so-called computer without a network card is as good as a brick to me.
The idea of a Web Browser being "essential" to an OS is to mean that the OS itself would not be complete without this specific browser, which is in fact not true. Whatever combination of OS + browser you elect to use, or of you eschew the common OS parts in favor of it being entirely browser based is your choice.
That is the contention when Google, and also when Microsoft, try to claim that their respective browsers are essential to their OSes. (Before anyone tries to call me out, yes, Apple is just as silly with iOS, but at least they attempt to have some very fragile ground to stand on regarding performance)
So the argument isn't that a web browser isn't essential to modern day computing, it's that the OS itself does not need a built in one to be complete, or any specific browser to realize its goal of being an OS.
MS argued that the specific web browser IE was essential and I think that's the type of argument that is problematic, both for MS and Google
Internet Explorer and the Windows shell were the same code. There's a reason why until this day the Windows shell is `explorer.exe` - it and `iexplore.exe` (IE) were the one and the same. You could open a file explorer to C:\ and then type in `msn.com` in the address bar, and the PC wouldn't blink.
The short answer, at the time anyways, was that you could just delete it to no consequence. It was just another program.
Some of the phones do "need" a browser as they provide it as a feature to apps, so things are a bit murkier now.
And there's the WebView component, that's part of the SDK, that's essential, and it can be a dependency, or it can be bundled into the APK. (There's even https://crosswalk-project.org/ that is basically new WebView for old phones - Chromium built for old phones.)