I don't need to pay tolls, but I frequently stop for coffee or a sandwich on the road and having a supply of coins that aren't in the bottom of my pocket is handy. I frequently pay for small items in cash.
As for the wallet, I find it very uncomfortable to sit on it and don't feel the discomfort is the price I should pay, every time I drive, against the possibility of being in a wreck and unconscious when they find me. They'll figure out who I am quick enough from the license plate on the car.
As for police interactions, I'm 60 year old white guy with grey hair, driving a late model vehicle in good condition - not the type that usually gets shot by the police. Besides that, I learned a looong time ago (or is it just common sense?) that each and every time a cop pulls you over they are going to want to see your license, registration, and insurance card. On the few occasions I have been stopped by a cop in the 40+ years I have been driving, I've had the documents out in my hand before they every approached the car. I suggest you do likewise- it may prevent you getting shot.
One more tip- don't argue with the police. No good can come of it. Be polite, say thank you, and move along.