Except web browsing, which is a huge part of software engineering, and which is nearly impossible to do without the mouse because most websites cannot be reasonably navigated with shortcuts alone.
So the whole model falls apart, really.
Not that I know everything, but I view informational browsing as a distraction while programming. The LSP augments most of the knowledge gaps for me.
If vim isn't for you that's cool. But I find other editors for me are this-is-fine.gif.
Really, the model doesn't fall apart. But you don't have to use it if you don't want to.
Most of my operations on a web browser involve scrolling or swapping pages, which I typically do with a keyboard. Besides every browser has keyboard extensions that allow one to select links through keyboard press. Being a neovim user I like vimium on firefox. I also like to use text based browsers for a better browsing experience and less distraction when I am coding.
The point of using Vim, is that you boost your keyboard interface to the maximum. Obviously, using Vim, means you touch-type. Also, you don't use the mouse. Basically, using Vim, is like having the brain hard-wired to the computer for every task, not only text edition. Everything you do goes through the keyboard, and you don't have to think about it. You scroll through text, search for it, edit it, open new files, etc.
For instance, most of the time I don't use any GUI for Git either. I do everything in the terminal, and only use the GUI for partial commit (ie. select which line to commit). I have dedicated aliases for getting history, etc.
Also, when learning Vim, you notice that many (Linux) tools have Vim shortcuts enabled. I discovered many of them by chance, out of the habits of using Vim shortcuts.