Preface: Recognize that the mound isn't really a mound. It's an elevated pitching plate. Any momentum you get toward the target, when using this type of structure, has to come from the pitcher. Using a straight up lift means you will eventually have to change direction to move toward home. In a strict physics sense, any change of direction has a pause or stop just before the direction change...aka zero momentum. This makes anything done before the direction change become valueless. When momentum is the most useful, it's built up along the way in what we call a kinetic chain or kinematic sequence.
I'll try to break down a first step towards improving his delivery.
Jackson seems to treat the rubber like it's made of glass. He's being very careful and cautious on it. He's starting from a wind up and it looks like he transitions to a set position. If he's not going to derive any benefit from using the wind up, he should simply pitch from the stretch.
Side Note: One thing that I absolutely hate about the direction the modern wind up has headed is this step to the side of the rubber. If there is no rearward component, even the smallest one, then there is no reason for you to use the wind up at all. All this does is create lateral momentum into the leg lift. This is also of absolutely no benefit to the delivery. The rulebook states the pitcher is allowed one step back and one step forward during the wind up. This is now a rule that is not enforced because pitchers started stepping to the side and now some even have a small forward component to the free foot before turning and repositioning the pivot foot. Pitchers who employ this sideways first step, eliminate a windup pick off move from their arsenal because a step toward first from the windup looks too much like their delivery to the plate and umpires call it a balk even though it's a legal move in the rule book.
When I teach leg lifts, I teach the pitcher to keep the hips high (preventing post leg collapse) and thrust them down the target line as they try to get a maximum leg lift. These happen together and not in two actions like those who teach tall then fall, or lift then drive.
When you do these together, in my opinion, it allows the pitcher to break his hands with his hips and posting foot having the largest amount of separation (large angle of attack) and with more aggressiveness and speed--which is kind of the point of the whole delivery (get the arm speed up or maximize the degree seconds on the throwing arc. By having a lift/thrust first movement, the pitcher has less time to get the arm from hand break to full cocked. This forces the pitcher to compress into a smaller time interval the distance the arm needs to travel...pretty much the definition of velocity.
Often when pitchers are taught segmented deliveries, such as balance point teaching, there are several pauses and stops during the entire delivery. As I explained before, no accumulated energy is carried beyond a pause or stop.
My way creates aggressive, fast movement down the mound, explosive hand break, and maximum arm speed getting into foot strike. This is making great use of the lower half movement before the delivery shifts into becoming rotational and the kinetic chain can build on itself. The more speed you can generate before the first rotation, provided there are no breaks in the kinetic chain into release, the more exit velocity a pitcher will achieve.