You can read about their architecture in their discussions of Spokes, which replicates repository networks (the original repository and its forks) across data centers. eg: https://githubengineering.com/stretching-spokes/
Trying to put all of GitHub's object files in a single packfile - even just putting them on a single server - would be impossible.
But even on hosting providers with a bespoke implementation - that do not use core git to manage Git repositories - this would be challenging. We have a custom Git server implementation in Visual Studio Team Services, but it still makes sense to shard object storage with the repository: you have to worry about scalability and performance, but also things like data sovereignty. We can't just put a user's git repository in some global SQL Azure database that contains all the repositories in Visual Studio Team Services: the repositories need to be geographically located with the VSTS account they created.
Puting whole github in single packfile is obviously impractical, but having whole github on some bespoke Venti/IPFS-style content addressable object store is not.