I rarely carry a rifle - any rifle- with the chamber loaded unless it is in my hands. I can't honestly say I've missed any important opportunities, but I can say that I have had a few loaded chamber "what-ifs" mostly prior to adopting that practice.
As for shooting once or more than once, I do it all the time if the animal doesn't go down immediately. A second bullet is never bad insurance whether needed or not. I know some folks have a sense of pride in "doing it right one time." I left that behind nearly three decades ago when I moved north. I guess I never really thought about a single shot being at a disadvantage when shooting a second shot. I suppose one box of ammo per year or only bench work with the rifle could create bad habits or prevent the good ones necessary though.