There are already multiple established solutions (which are noted in other comments) that are free, paid, open-source and closed source with large communities that solve this problem. At my last company, we had an Ubuntu machine running our git-server and it solved the issue you're saying.

Edit: You know what would make this awesome. If this project could some how extend GitHub via the API and somehow replace GitHub when it goes down. Sort of like a private HA solution to GitHub incase of an emergency. Now THAT is something that I'd look at and say "okay this solves a new challenge with the current state of hosted Git platforms."