If you're already spending a lot of time in the browser looking at stuff (AWS Console, Stack Overflow, etc), I can see the convenience of just switching tabs to your terminal rather than pulling up a window.
So far I've solved that problem with keyboard shortcuts or other macros to pull up a terminal when I need it.
Conceptually, I don't think the solution to "switching windows is too hard" ought to be "make the terminal part of the browser". Although it does seem like perhaps the least immediately painful way to solve the problem.
Using Lynx in the terminal might be another way to do it.
I think getting the terminal into the browser is exactly the way this should be solved. Currently I'm in a browser for the vast part of my work, as are a huge lot of other people. Most of the web apps I need wouldn't even render in Lynx.
So far I've solved that problem with keyboard shortcuts or other macros to pull up a terminal when I need it.