The problem lies in the comments and issue tracking, which are not stored in git. Sure, you can clone the repo, but you can only take the wiki with you, the rest would be lost.
So what I'm hearing is the solution to this migration problem is to also store the entire issue tracker as a git repo alongside the real repo and wiki repo? Git repos for all the things! (Seriously, I think this solution would fit right in along with the way Wikis are handled)
To my mind, the actual problem is neither one of those things, but if Github is wrapped up into some new project. Many of the citations for Github aren't for software, but as a stable, open store for data.
Which means if that URL changes, that link - in a physical paper - goes stale.
If you need stable links then buy yourself a domain or use a URL shortener that you can update. Might be wise to also provide content hashes of the data you're referencing in your paper.