I never saw/heard of evidence of such behavior.
> but you'll still lose your emails if they decide to suspend you
Emails are easily backupable, you can download them locally and/or forward everything to the "backup" email. One more service to host email on your own domain is Yandex.Mail, it's free and pretty good.
I'm personally considering hushmail (Canadian) or some other paid email in the future, for maximum piece of mind, any double digit number seems reasonable enough annually. Some out of the way liberal first world country , no superpower (and superspy) aspirations, a small paid provider (that actually needs customers and word of mouth and not throwing their weight around, Google is notorious for deleting YT channels willy nilly for 'guidelines violation' and then restoring them after a shit storm) to ensure no 'smart' 'ML' algorithm bans you. Sounds just about right.
I was quite surprised that my gmail account was banned without doing anything remotely malicious. (Certainly not anything listed in https://www.google.com/intl/en-US/%2B/policy/content.html) I suppose it's my word against Google's, which isn't a happy position to be in, but to the best of my knowledge that's what happened.
Regarding other services, I was hoping to get some recommendations about which one everyone likes using. Gmail and FastMail seem to be the two HN favorites, but FastMail gets expensive quickly for side projects. You can host your own email, but people have shared some unpleasant experiences with that route. It's true that you can still use gmail without losing your address, but you'll still lose your emails if they decide to suspend you.