That's not really true. You're using a third party to send out messages, and if you don't like it, you can switch pretty painlessly. You could even use you're own local MTA at the same time, if you really wanted to.
The IMAP/POP3 server is yours, and all the email is stored on something you control.
This is what I do but I use Amazon SES to send out mails from my selfhosted email infra. All emails pass through and I have the satisfaction of knowing I can just switch to another provider if SES shitcans me.
The IMAP/POP3 server is yours, and all the email is stored on something you control.