Using the carrier's SMTP server will not work when trying to send email when the iPhone is connected to an available wi-fi network unless the carrier's SMTP server is authenticated.
My Exchange admin could choose not to have the outgoing mail server authenticated and if so, I would not be able to send email with the account unless I was connected to our wi-fi network at the office.
If the email account provider has an authenticated SMTP server, it will work without fail unless the ISP the iPhone is connected with has some over the top and very unusual restriction.