I once saw a hardcore emacs user forced to use vim because he was building a setup that allowed shell users to edit a file. And couldn't do that in emacs. So he had to use rvim -y.
I myself once built a nethack shell server where I used rvim to allow users to edit their nethackrc.
So distros preferring vim can either stem from it being vi-compatible which is POSIX. And/or from having a restricted mode.
I would entirely agree that a lot of vims popularity lies in it being part of the default install on pretty much every unix box ever though. That and it actually being a decent editor once you get over that initial insert mode/command mode learning curve.
* http://pubs.opengroup.org/onlinepubs/9699919799/utilities/vi...
There is a whole history of why emacs is not likewise in the SUS, already related long since by other people.
The quickes way to validate this believe was to look for the Ubuntu package sizes (look at the size (installed)):
https://www.cesifo-group.de/DocDL/dice-report-2016-4-li-niko...