Yes of course I ride with ID.
I have a zip pouch for cycling that goes in a jersey pocket or wherever else- it has a little cash and a copy of my health insurance info. I move my DL and a check card to the wallet for each ride. It also holds my phone and is waterproof, so everything is together and access is easy.
To me the question should be- why should I ride without any ID? I think answers will not be very compelling.