Neat hack, but IMO this just loses waaay too many features and UX that Github et al. have. Only masochists will use this. Here are a few I can think of:

1. From a user perspective it's "simpler" in that it saves maybe 1 command... git push (I've still going to want to make a branch), and clicking on the "create a PR" link. But you've also made updating a PR way more of a pain - it was git push, now it's... I dunno some long command I don't remember and looking up a PR number in the web interface?
2. Can't request reviews from people.
3. Can't enforce review requirements.
4. Can't require review comments to be resolved (I bet it's easy to miss review comments!)
5. Can't easily tell who wrote review comments. Are you really supposed to have a conversation by adding // Dave: I agree under comments?
6. Can't add comments to code that doesn't support comments (e.g. packages.json)
7. No CI integration.

I guess some of those are fixable, but overall this seems like a clever hack but very clunky.

I guess it's better than a mailing list at least.