I agree that's how it should
work but, knowing BT, I'll need to check if ever I should decide to move.
Even registering for the online-only version, you still have to go through the full rigmarole and it's regarded as a "proper" product. From the email:
Thanks for choosing BT Sport
This is to confirm your order, what you're getting and what you need to do. Please keep this email somewhere safe because you might need some of the details later.
BT Sport Pack £12.00
Get the best BT Sport deal with BT Broadband - www.bt.com/packages
FREE BT Sport Pack £-12.00
For BT Broadband customers
Your monthly total £0.00
Section 41 of the BT Sport T&C
The discounted rate for BT Sport will last for as long as you are within your minimum contract term on a BT Broadband contract. When your minimum term ends or if you cancel or end your BT Broadband contract during the minimum term, you will start to pay the standard monthly price for BT Sport. Any credit or debit will be detailed on your bill.
To me, that says when the minimum term of the broadband contract runs out, you start to pay for BT Sport even if you renew the broadband ( or don't cancel it).