it never hurts to have all those administrative details in place, but I've not had proof of insurance asked for. As I said, passport and a couple innocuous questions. I've not taken firearms through, but can see that changing things. A lot probably depends on who is on duty when you pass, how crowded it is and what they do to speed things up, and the sort of day the agent is having.
Two years ago i "won the lottery' and had to go inside for extra scrutiny based on a random system. Biggest problem it was about 7:30 with shift change going on. Took an extra hour out of my travel.
