actually they are more sensitive to imbalance , 1 oz of weight not in check will rattle your teeth out of your head , as the tire grows and the imbalance moves outward ( most of the tire mass is in the tread and first inch of the sidewall next to it ) , we try to get them as close as possible by breaking the bead and rotating the tire to get a nuetral before adding weights , I had a weight come loose from the rim during a burn out and first I thought I kicked a rod from it being thrown against the wheel house , and then it started to shake violently . if you look at a top fueler rim every once and a while you will see the duct tape over the stick on weights . the tires start out at 33-34" and can grow to 40 + " in diameter . My 32" tires will rub a 36" wheel house and they are stiff walled and run a rim the same width as the tread
I think the idea of not balancing new tires is based on the quality of the tires available in the '50s and '60s. I don't think it was all that strange to have belts "slip" to a different position as the tire was mounted and put into use for the first time. These days tires are held to better production standards; they shouldn't do as much moving around as they wear in.