I suspect the answers would be: use non-arrow keybindings for browsers (e.g. vim-like plug-ins, or alternative keyboard shortcuts), remap your terminals keys (maybe, use a different terminal entirely?), use insert mode for only inserting text.
I use a “vimium” plug-in for Firefox and I quite like being able to go up/down with j/k. Though I still use the arrow keys for my terminal.
Yup I've just installed vimium on chrome, and it seems to do the job.
I've tried out vim-mode bash in the past, but much prefer the default emacs-mode on the command line, despite being a vim user.
Either way I'm suspecting a ton of exceptions which necessitate resorting often to the cursor keys, however (like another commenter has mentioned w.r.t various GUI apps).
I use a “vimium” plug-in for Firefox and I quite like being able to go up/down with j/k. Though I still use the arrow keys for my terminal.