tl;dr email isn't needed, people are just used to it.
It's a fair point, and perhaps its one that the likes of Apple SignIn should solve. On the one hand, even Microsoft and Apple send me heaps of spam under the guise of "communication" and I don't want them to have my email address if I can avoid it. The OP says they have trouble with support, but they can (and it sounds like do) tell people to just check their Apple email. Most places that I contact for support require me to put in a contact email for that ticket because people use throw-aways anyway. As for security problems, well I'm glad you're one of the few companies to actually disclose security breaches. But if the information on the website is actually sensitive, then there should be additional checks to begin with. If it's CC info, you should contact the CC company, there should be 2FA, there should be more than an SSO service, which already prevents the biggest and worst security breach of leaked passwords. In short, I doubt the need to contact a customer unsolicited is so great, common, or difficult as to require that a user disclose a non-obfuscated email address, which people already commonly have throwaways for. And the reason they have throwaway accounts is because 99% of the time, when I give someone a ...@spamgourmet account or whatever, that address gets spammed, even though I told them not to put them on the mailing list (because they share the email with third parties, or just plain ignore it).
The tradeoff is a bad one. I do not have sensitive information on Reddit that is not public. A private investigator could probably deduce who I am by looking at my Reddit posts, figuring out where I live, where I went to school, what family members I have, what my job is. They don't need to contact me urgently about a security breach. You can say when I sign on and lock my account until I acknowledge it, but it's not urgent. Even a website that might need sensitive information and, for some reason, doesn't want to require I actually verify my identity for real to upload that sensitive information, that doesn't mean I'm using the website in that capacity and should give up identifying information in case I need to give up identifying information later and you need to contact me that my information has been leaked.
The perspective is worth thinking about, but I'm unmoved that it amounts to pushing the needle to "you need my real, primary email address." I believe the tiny, tiny minority of companies that actually need that and shouldn't just rejigger their system to better security and privacy practices to start with can find reasonable workarounds or resort to mild inconveniences like requiring a callback number on support.