Curious if you (or anyone) can explain why this is necessary, specifically how this differs from setting it through the Default Applications in the Settings Panel.
Hate to say it but if you have to ask this you may not really understand my answer. But I am going to try to answer and keep it simple.
This is necessary because of the way we created the desktop file for the appcenter. It is located at /usr/share/applications/bodhi-appcenter.desktop. This file contains the line:
Exec=x-www-browser http://appcenter.bodhilinux.com x-www-browser calls the application configured to open a website on any desktop environment that runs under X Server. We use it as it is a well-known Linux standard guaranteed to work on a properly configured system with a properly installed web browser. We could have used other options such as sensible-browser, a Debian only standard (and package, has to be installed to work). But sensible-browser on Bodhi ends up calling x-www-browser anyway. I also could have used gnome-www-browser or www-browser, assuming these are set. But gnome-www-browser is primarily a gnome thing ... I am not going to go over all possible options here, we choose x-www-browser because it is a well-known standard.
As far as setting it through the Default Applications dialog in the settings, this actually sets the application used by xdg-open and enlightenment-open to open a URL. This is based on mime type. We decided some time ago ( a few years ago) to not use xdg-open or enlightenment-open to open our appcenter or our quickstart guide because when a user installs and uninstalls applications these applications 'mess with' mime types. At one time we did use xdg-open (or was it enlightenment-open ... I forget exactly) but then users ended up with weird things happening like our quickstart guide opening with geany and not a web browser. Users who had limited Linux experience and did not understand Mime types were on our (old) IRC channel or forums wanting help fixing it.
With x-www-browser this is not going to happen as long as they have at least one web browser installed that adds itself to the x-www-browser alternatives list then the appcenter and the quick start guide are going to open in a web browser, regardless of how many apps the user has installed that like to add themselves to the various mime types associated with URLs, URIs, HTML, et al. Most web browsers installed via our repo do add themself to the x-www-browser alternative list. Certainly all the better-known ones.