There's no reason to learn vi if you know Emacs. If you claim that Emacs isn't installed everywhere, guess what: Neither is vi.
If you want an "installed everywhere" editor, learn ed. If you're willing to take an editor with you (or otherwise make sure a specific editor is everywhere you are), there's no reason it has to be vi.
I can't remember ever encountered a unix-like system without "vi" installed. I've used (and set up) machines running FreeBSD, DragonflyBSD, OSX, Ubuntu, Debian, RHEL, ...
Plenty of those didn't have emacs, especially on first boot, when you're most likely to need to modify network configuration files in order to get online to install new packages in the first place...
Edit: By "vi" I mean that somewhere in the path there is a program called vi. Of course, usually this is nvi, vim, evil, etc; I don't mean the original UNIX vi binary.
I've used ed(1) to do complex(ish) programmatic edits to files that I think would have been extremely painful otherwise. An interesting editor worth spending at least a small amount of brainpower on.
I don't think this is true. I've certainly been in a bunch of hairy situations over the years where I had nothing fancier than ed available to me because I was in some sort of recovery mode. The single user mode that FreeBSD comes with is lacking vi if, for example, you don't have / mounted yet. Thankfully ed is in the ramdisk.
V7/x86 [1] has both vi and ed, but ed is easier to get to.
"Of course, we are not absolutely compelled to use ed, since V7/x86 comes with the full-screen editor vi (as well as the related line editor ex), but getting access to vi in this context would involve mounting the /usr filesystem and changing various environment variables and settings to allow editing in full-screen mode. Some basic ed skills are particularly useful in the V7 world, and most of all when one is involved on system administration tasks." [2]
I much prefer emacs and at least emacs shortcuts are by default in most shell (and everywhere in osx!) but no, every servers I install (debian, ubuntu, osx...) comes with vi but not emacs.
Anyone considering using vi should be warned away by this practice of "disagreement by downvoting". If they do it here, imagine what they would do to a bug report!
If you want an "installed everywhere" editor, learn ed. If you're willing to take an editor with you (or otherwise make sure a specific editor is everywhere you are), there's no reason it has to be vi.