[AnthonyMouse]

Isn't that fairly common? You could then put in some other address, but you could do the same thing by setting up your own mail server, and in the former case you're not even really anonymous because the headers are going to show it was sent through their mail server and their mail server's logs will show which account was used to send the message.

[afiori]

The email sent from your own separate server will fail basic dmarc/SPF/dkim validation the email sent by their own servers likely will appear legitimate

[AnthonyMouse]

It would fail in the same ways unless the from address you're using is on their domains, which is then only a problem for their own customers rather than innocent third parties, and their own customers have the sensible option to stop using their service.