it just doesnt make sense, look and nolan ryan, sandy koufax, roger clemens, all with impressive fastballs and long term arm health.
your legs are what drive you foward, and your stride is longer when your lower than you are when your higher, i understand how you dont kicked off the back rubber, but your legs is where you get your power, look at 95% of mlb pitchers, they have tree trunks for legs, there huge.
The common reason for “staying tall” that I hear is to get a downward trajectory on your pitch. But I agree with you, there are other important factors to consider.
to get good downward plane and momentum. You also use your legs when staying tall and falling. You land with your front leg bent and then when you release the ball you get extension ofthe front leg which provides power. Although pushing off the mound gives you better velocity it causes you to sling the ball and can easily cause overthrowing. Plus it is harder to get good downward bite to your curve ball. with a longer stride causes more velocity but you need good leg strength to do that. That is why power pitchers all have very big and powerful legs to allow them to have that long stride.
I wouldn’t exactly say that Koufax had long term arm health, although he was very overworked he also has to retire because of an arthitic elbow. If you watch film of power pitchers you will that stand tall and fall method of pitching.
There are two factors that need to be considered: the type of pitcher you are, and the height of the mound. One day the Yankees were playing in Kansas City, and Chien-Ming Wang was pitching, and he was running into trouble in the first inning. Jorge Posada called time, went out to the mound, and advised Wang to shorten his stride. The reason for this was that Wang is a sinkerball pitcher, and the mound in Kauffman Stadium is lower and flatter than any other mound in any other ballpark—disaster for sinkerballers! So Wang took Posada’s advice, shortened his stride, and went on to pitch seven strong innings and get the win.
I learned from watching what the Yankees’ Big Three pitchers did, way back when—they drove off the lower half of the body, using the legs, the hips and the torso in a seamless motion, and that is how you get the power behind your pitches. 
look at sandy koufax’s # of pitchs in a game, back then, 150 pitches was common for one pitcher and was expected back then.
and by fall, do you mean just the upper half of your body ( bending over)
or do you mean fall as in letting your legs fall toward the ground and plate.
I figured id come back and post on this topic from my game one of my games. since coming back from acl surgery ive been messing around with my mechanics alot. usually i load up before i throw(really need to get some software for vids) to show my backside to the catcher.
Then for some reason i started keeping everything level and go more direct to plate. I was trying to save my elbow because i pinched a nerve. i was keeping my weight back but not bending at the knee or trying to overcoil. when you stay tall you actually feel very tall and in alot more control over your body. after 2 innings i started staying tall but bringing my front side turned a little more and creating the coil. increased velocity and explosiveness.
Ive done this before but overanalized mechs and kinda forgot about it. staying tall is exactly you would think, when you bring your leg up make sure to remain on that back leg as if it were a tree trunk. it doesnt bend until descent and bends to maintain control over the fall. this also increases stride length because your waistline is further off the ground during stride as upose to drop and drive method.