I believe that this does not really address what "essential" means in this argument, and I find you're both arguing the same point but semantically disagreeing.

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.