From MN here, and 'registration' is a weird one for me. "License and Registration, Please" is a phrase I've heard all my life, but never have I ever needed to present the vehicle's title, or the paperwork that comes with the registration tabs. The tabs go on the plate, and the paperwork goes into the tax folder in the filing cabinet. While I do not have tremendous amount of experience being in accidents or breaking the law, I've NEVER needed anything other than my license and proof of insurance card.
Same idea with the insurance cards, I can't imagine trying to keep the cards or the registration paper in my wallet. I have 6 vehicles, that would be insane. Insurance cards go in each vehicle's glove box (or in the case of the bike, in the seat.)
If there's an accident serious enough that the power is lost and the glove box won't open, trading insurance information on the spot is the least of my worries.