Never heard about "transactional" emails before, but reading up a little on that now it seems that all these providers have TOS mostly for marketing campaigns plus the "transactional" emails, which are automated emails in response to some actions or stages in a customer initiated transaction with a business.
So, does using these services for "interpersonal emails" violate their TOS?
Also found this on reddit:
Keep in mind that "transactional mail" is very different from "interpersonal" mail and you need different providers for that. MailGun, SendGrid, Mandrill etc. are designed for transactional mail. They provide insight and analytics into the messages sent by doing things like intercepting clicked links, injecting tracking pixels etc. They can inject features like "unsubscribe" links into the messages. They can do things like scheduled campaigns with automated name insertion. They can detect bouncebacks and rejections from mailservers and keep track of blacklists of people or servers who shouldn't receive emails. This is good for automated messages, notification emails, newsletters, marketing campaigns etc.
These features aren't appropriate for "interpersonal" mail, and in particular you don't want to have things happen like "mail bounces for one user that one time and now it's on the automatic blacklist, and nobody in the organization can send mail to that domain anymore".
For interpersonal mail, you need an anti-spam gateway that also handles relaying outbound mail for you. E.g. Office 365's "Exchange online protection" service, Barracuda, Proofpoint, Mimecast, etc.