Many websites and services offer 2FA by using an authenticator app, which is widely regarded to be more secure than via SMS. I use my authenticator for accounts wherever possible.
As a cutting edge technology company, why can't BT offer this option instead of or as well as the SMS and email methods?
What on earth gives you the impression that BT are 'a cutting edge technology company'?
I've dealt with them as a consumer and a business customer for over 30 years and I've never seen anything to lead me to that conclusion.