That's not true. I run my own email server for 15+ years now. There are only 5 of 6 mailboxes. I never had a problem with any other host. Not Microsoft, not Google. Maybe, the reason was, the IP was also 15+ years assigned to the same domain. I have only known senders, family and friends.
The last days, the hole subnet was blacklisted on some blacklists. So that was not my fault, the growing business of the provider lead to this situation. Eventually I moved to a very small provider and run a mail cow on a vps. On a fresh IP without any reputation. Same 'customers', the only issue was with T-Online in Germany, but a mail solved this. To keep this kind of issues away, I use sendgrid as a SMTP forward. With only a few mails per day, this is free. Mailcow provides a lot of features, rspam filtering, a lot better and faster than spamassin. Active sync, imap, webmail, everything. Solid backup, runs without any problem.
Don't forget, iMessage is not using SMS. It's like WhatsApp or all other messengers, but Apple only. It uses the same app, but that's it. And yes, no one pays for texts, because all plans have texts included. Some prepaid plans maybe.