I understand this linke of thinking might suit you but I fear it is not as convincing as it sounds to you. At least it's not to me.
I think therefore it's pretty much inevitable that if you need a more advanced code review tool you'll end up picking a third party one. Though admittedly, as the founder of Reviewable, that thinking does rather suit me too. ("It is difficult to get a man to understand something when his salary depends on his not understanding it" and all that. :D )
If i must pay for GitHub and an external tool, isn't GitHub just an dumb overpriced git storage.
Not to mention that you get an easy way to spin up your CI/CD workflows in GH Actions (which of course definitely has its own problems, which there was another popular HN post about recently). There's a reason why it's the default for new companies -- if there was something much better, it wouldn't have the market share it does I think. Familiarity coming from OSS is also important.