I was under the impression that you have to confirm your email address when you subscribe, but I could be wrong. There’s also an option, as sender, to unsubscribe folks who haven’t open your newsletter in a while.

Another route would be AWS SES. They have a free tier. For managing the subscribe/unsubscribe process you could still use MailChimp or a self-hosted solution like Keila https://www.keila.io/, although I have no experience with this.