Azure is self hosting. If you have on-prem, it makes sense to host on physical gear, but most startups aren't at that phase of their lifecycle. GHE vs GitHub for me is a data lifecycle decision, and even with GHE on Azure, you have more control over your data than in public GitHub.

Influencing factors can be regulatory, policy, SLA, that sort of thing. A prior employer had a blanket policy against intellectual property in a public service no matter the security, for example. GitHub has reliability issues lately as well.

One practical thing I've heard is that it's really easy to accidentally make a repo public on GitHub (I agree).