We recently got locked out of our email account for breaking Rackspace's email policy for sending bulk emails outlined here - https://docs.rackspace.com/support/how-to/best-practices-for-sending-emails-to-many-recipients. Apparently they've taken some stronger steps to try to stop spammers from using their servers, and the automatic emails our store sends tripped the new spam detectors. We were unable to convince them to make an exception for us.

We've since been forced to move to a third party email sender, MailGun, although there are many others you can use. This seems to be the new preferred way to send what they call "transactional emails" (like email receipts that are sent automatically on checkout, or shipping notification emails) rather than just plugging in your regular email credentials and having the site establish an SMTP connection.

MailGun allows you to connect via SMTP, so we were able to get up and running pretty easily by just plugging in the new credentials. MailGun also has an API you can connect to programatically that allows you to do more with it. It might be nice for a future update to include a method of sending emails this way (using MailGun or some other bulk email provider) rather than SMTP.

My personal thoughts are that if a host will not allow you to send email receipts and normal business communication necessary for an e-commerce store, then they should not be hosting e-commerce websites.
I would seek a new host.

I understand they may not want you sending promotional email campaigns, but for just email receipts and normal communications, that seems out of line to blocks those.

The cart does integrate with Mailchimp and they are good for sending your bulk promo emails.

David

Yes, we weren't happy with them either, but from our research it seems like a lot of email providers are doing this. They're taking the position that any automated email is likely spam, I guess trying to put it on those bulk mail providers to do the vetting for them rather than doing it themselves. Oh well, what do you do...