WOW, I just saw this thread and voted and was surprised it's like 75% would rather ride a bucker.
I guess it's because, to me a rearer is so simple to stay on. You just keep yourself vertical to the ground by moving your upper body forward.
My Uncle bought one horse from a lady, a leopard App, he had learned to rear and on the third rear would flip over backwards, break the saddle. Everyone was scared to ride him so he didn't get ridden.
My Uncle did love be but put me on him and told me: first rear you lay into him and move him forward and work his butt. First the crop back and forth across his neck right infront of the saddle, while yelling and growling until he quits the rear. You want him out of the rear and moving off immediately then, work him and make him sweat.
I took him for a canter, we did figure eights, spiiral in and out. We went to the trot and did some more of the same in that gait, until he was blowing a bit and starting to tire. Then walked on back to the place he reared at.
I did that the one time on the first rear and he NEVER tried it again.
My uncle said: They can't rear very well when they're working, it's easiest for them to rear when they're standing still but, they can buck whatever they're doing.
Rearing is much easier for me to ride and cure.