The point is that the trade-offs usually come down in favor of using GitHub Enterprise (or whatever other well-regarded, trusted enterprise system). The availabilty and uptime are your own, because it’s self-hosted, like git. The data integrity is also your own. The security is better than probably any other VCS interface over git, with the possible exception of GitLab, and almost certainly better than what an organization could come up with on their own if it’s not their core competency. Unless you’re literally using straight git, GitHub Enterprise (or again, whatever other competitor) usually enhances team productivity. The attack surface is larger than git, sure, but the rational solution to that would really be to use no interface over git, because GitHub Enterprise is as safe as they come.

I think you’ve misinterpreted people’s reactions. It’s not at all controversial to use other companies’ services for your most sensitive assets, it’s your opinion that appears controversial to them. If you’re in control of your own servers, what remains is to trust GitHub Enterprise not to literally phone home your source code or to enable remote code execution on your own server. There are myriad information security policies and compliance methodologies for compartmentalizing, quantifying sharing that risk.

For what it’s worth, having personally performed security assessments for over 50 different companies across the gamut of size/maturity, nearly all of them use a centralized VCS hosted or produced by GitHub or Bitbucket (and nowadays, occasionally GitLab too).