For NatWest you don't need it for logging in, you only need it (from what I can remember) to set up a payment. So I can add a payee to my account and need the card reader to do that, but I don't need the card reader to make the actual payment, I don't think so anyway.
Wot you said plus you need it to change payee details and some payments will always ask to use the reader.
I have three monthly payments I make with NatWest, one never needs the reader, the other keeps changing the payee reference so I need the reader (to both change the ref. number and make a payment) and the third always asks me to use the reader.