You can mask your email address in git commits but a lot of open source projects won't accept that. And some pseudo-open-source ones insist on sending you an email to authenticate before they'll give you access to the GitHub repo (looking at you Unreal Engine!)
So, no, I don't think they could simply "not show the email address".
To his point, you can set that to the no-reply email address GitHub gives you if you don't want mail but do want the commit to be linked to your GitHub account.
[0]: https://git-scm.com/docs/git-commit#_commit_information
[1] In practice, it's a bit more complicated. Merkle trees are involved, so it's hashes of hashes of hashes instead of hashing a multi-gigabyte blob on each commit, but that's a performance optimization that doesn't affect semantics much.
There's never been an obligation to use a real email address for git