There's a few reason going up off your left dribble as a right handed shooter works better.
There's less movement in your shooting arm, particularly your elbow. If you come off your left dribble into a jumper, as your left hand bring that ball into your "shooting pocket" if you want to call it that, your right elbow is already tucked in and facing the hoop. When the ball hits your right hand all you have to do is go straight up with it. It's quicker. Off your right dribble, there's much more movement, and your arm from down at your side has to go up, bring your elbow in and then go up all in a fluid motion, while still having to square up. On your left you're usually already closer to be squared. It's practically twice as much movement for your shooting arm, which means twice the opportunity for variation in your form going off your right dribble.
The other aspect is that right handed players jump better of their left leg. It's always that way. You grow up having used your left foot to explode. If you go up off your left dribble, you plant your right foot first, then swing your left foot over and explode up. Your left is providing most of the explosion here, and it's why most right handed shooters elevate more off the their left dribble. Looking at what you posted, Reke is no different and gets more elevation off his left dribble. The reverse, off your right dribble, and your weaker leg, your right, is responsible for more of the explosion. Hence, he seems to kick more and fade more off his right dribble.