Browser extensions are useful. I've made some simple ones and published a few:
https://addons.mozilla.org/en-US/firefox/user/14310707/
But it's also worth considering where the browser gives priority. For example, while browser extensions can add custom keyboard shortcuts, they can't override the keybindings a website uses. Want to use the keyboard shortcut Ctrl-Shift-1 for a browser extension while a Google Docs page is focused? Nope, sorry, can't be done.
https://github.com/gsomoza/firefox-easy-container-shortcuts/...
It's pretty clear that while a browser extension can access browser APIs that a web app can't, the extension is still a second-class citizen in other respects.