Domains are cheap; never use an email address that's email-provider-specific. That's orthogonal to whether you host your own email or use a professional service to do it for you.
I will lose some email history, but at least I don’t lose my email future.
However, you can’t own a domain, you are just borrowing it. There is still a risk that gets shut down too, but I don’t think it is super common.
I back up all my email every day, independent of my hosting provider. I have an automatic nightly sync to my laptop, which happens right before my nightly laptop backups.
I self host my mails but still use a freemail for the contact address for my providers. No chicken and egg problem for me.