There is a good difference between a sysadmin's workstation and/or what I'll call "management servers" - those we use for our own tools and whatnot, and those that we keep up for production use, where uptime is critical and knowing exactly what is going on is paramount.
I use emacs... all the time. It's my favorite editor, bar none.
I use vi/vim every day, because it's always there.
It's not that no file should ever be edited there, but, especially in today's clustered world, it's good practice to keep your servers as minimal as possible.
It might sound silly, but keeping to principles and controlling as strictly as you can get away with the changes that go into your production servers is a good practice that tends to keep things working.
vi is handy because it's always there. Emacs is fine - but it only REALLY shines for me when I have my custom environment set up - for a quick edit, it's just a quick edit.