Having switched to Kak recently, I've found this painful since I sometimes SSH into machines with only vi installed and so have to switch back and forth between kak and vi; it's a real headache...and a real shame since kak's selection method is much nicer IMO
I find that I get irritated at vi / vim for not being as nice as kak, but vi is still useable. The hjkl keys still work, :w, :q! and so on are still the same. I, i, O, o, P, and p still do the same thing. Basic movement is almost the same except you don't get selection with your movements. I tend to fall back on this common subset when I'm using vi. Marks are different in kak, so I don't think to use those in vi. Same thing with ex commands. I'm more likely to use sed rather than messing around with vi's ex commands now.
The thing that confuses me most since the switch is vim's visual selection mode. I used to be a really heavy user of visual selection mode (V and v), but since selection is at the core of what kak does, vim's way of doing it seems really clunky now.
If I'm going to be spending more than half an hour on a machine, I'll probably end up taking a minute to build kak on it.
If I can SSH to a remote host I can use Emacs TRAMP mode to edit files or I can mount the remote machine file system with SSHFS and change the file locally.