This isn't about being caught without cash. Whenever I've gone to London I've used my contactless credit card to pay for transport, not because I don't carry cash, but because it's convenient -- you just hold it near the gate and go through; no need to visit a ticket machine.

A problem with this convenience is that you don't get any kind of physical receipt to prove you paid. Perhaps in my case, a ticket inspector could scan my credit card to check it was used to pay, but in the case of a dead phone, it can't be queried.