Thick cables cannot be coiled like that.
Mine was a long thick one. I wrapped it twice around my waist, and secured it with the padlock.
What I do now is to leave the U lock on the rack I use at the station. Leave the cAble with the lock. Of course that doesn't work if you're needing to lock the bike up at multiple places.
Do you leave your bike in a high theft area, where a U lock alone wouldn't suffice?
Or does your commuter bike still have quick-release hardware?