I've always assumed those emails are sent because if you forward a newsletter to somebody else, your personal 'Unsubscribe' link will still be on the bottom, therefore the person you forwarded it to could click the link and unsubscribe you from the newsletter without you knowing about it.<p>But with the unsubscribe confirmation, you'll know right away and can resubscribe if needed.
I like the positive affirmation that I have been unsubscribed. Yes, a web page "You are unsubscribed" is preferable, but an email confirming in subscription is better than dead silence.<p>I don't like the unsubscribe responses that tell me I will get email for 10 more days after I have unsubscribed.
To comply with CAN-SPAM mailing list unsubscription can't require a password, which means there's negligible security on it. Sending an email confirmation acts as a safety check that person unsubscribing actually is the email account holder.
Sending these emails drive down your domain's mail open rate and CTR[1], so it probably makes sense not to send those from that perspective.<p>1: My best guess is that if a user unsubscribes from a list, they aren't likely to open the subsequent confirmation email. If they are likely to open the email (use an A/B test to find out), then it probably makes sense to continue sending these emails, because there isn't any harm in mildly annoying a user that's decided to leave your app anyway.
I enjoy the affirmation that I've been successfully unsubscribed from a mailing list. Simply seeing "You're unsubscribed" on a web application just doesn't cut it for me.