In my 26 year career, I changed a ton of tires for motorists on the side of the road (that's one of the positive things we are known for). We carried the extra large 4 way lug wrenches just for that purpose. I bent a few (broke one) of those getting some lug nuts loose. Also had a few cars that wound up getting towed because I just could not get one or more lugs to loosen up.
I also came to the conclusion that the most neglected part on a vehicle is the spare tire. More often than not, when the spare was pulled from storage it would be just as flat as the one on the car. I started carrying one of the larger 12v air compressors just for those times. I patrolled a very desolate rural section of Interstate which might require 2+hr wait for a tow truck at certain times. That little compressor might have been slow but if the spare held the air, it got both of us back on the road quicker.