I don’t think they can arrest you as it’s not illegal to not carry ID. They can take you to the precinct until you can show some form of ID or otherwise prove who you are. Often they’ll leave your $5,000 Trek on the side of the road in the process “there’s no room in the trunk”. Cops can be pissy about some stuff and I dare say if it were the NYPD you would have gotten a ticket for sure. There’s a member on the roadbikereview forum who bike commutes in NYC, got 2 tickets for rolling thru 2 lights in Queens. The cops saw her on the first one and followed, then waited and stopped her after the 2nd. Possibly poor situational awareness on her part.

But you are right, 7AM ?, really ?.