I've been a BT customer for many years now, and have had the BT TV Sport add-on package since I signed up, which is now costing me £14/month after having been free initially.
However, I now never actually watch BT Sport on my TV, but only ever on the Online Player or the App (either on my phone or Playstation).
So my question is simply whether I still need the £14/month add-on to access the Online Player or App, or if I will still be able to keep watching BT Sport on there (because I do have BT Broadband) even if I cancel the TV add-on package?
The key part of your question is that you still want to be able to watch using the online player, and the Playstation app. These both still require a full subscription, which is currently £15 a month - so I recommend you stay as you are.