I have used it as well for the last couple of days (both on the tube's readers as well as in some establishments such as Pret) and found it to be working generally ok. I do agree with has been said above in terms of the amount of time it actually takes to authenticate and for it to work as desired - indeed, a contactless card is way faster.
I would say it is good however to have it set up on your phone in case one day you want to leave the house without your wallet! (Hopefully making sure that your phone's battery is fully loaded and the place you need to pay for have Amex contactless readers

. Now thinking out loud....you are probably still limited to transactions with a value of up to £20, so that kind of limits the things you can do.