The primary advantage they have over competitors is a trusted brand name. This name has been built, in part, by engaging and contributing to the open source community.
If GitHub were to open source _all_ of their software, some copycat sites may appear. These sites would not have a trusted name, thousands of well known open source projects backing them up and the expertise to properly run an instance of GitHub. As long as GitHub doesn't try charging users too much to use their service, there is no reason for people to use competitors to save a few dollars a month (reliability is far more important than a few dollars here and there).
Some open source projects may decide to operate their own infrastructure. However, this is highly unlikely because GitHub _as a service_ is much easier and more reliable than an independently managed instance. If GitHub can retain the open source community, they become "the hub" that everyone wants to be part of. As long as GitHub is known to support open source in a meaningful way, given the resources available, I'm sure they'd benefit from hundreds of open source projects improving upon and patching GitHub code.
I think they could quite readily open source _all_ of their software.