The Tall Kneeling Curl & Press and its progressions are excellent vertical press exercises, and ones I use with all my athletes who have healthy shoulders.
But the one problem that I see sometimes with some people, is a hyper extension of the lumbar spine when pressing the weight over head. Sometimes this can be due to poor shoulder mobility, which is can be caused by poor t-spine mobility, which in turn leads to poor upward rotation on the scapula, and scapula stability. I think if you have an athlete or client with these limitations, overhead pressing them may not be the best idea.
Other times it can be just a technique thing, or with a lot male athletes, too much weight. When guys try to boost their ego they will try to get the weight up anyway they can. This can lead to guys hyperextending the lumbar.
I have started doing this exercise in a 1/2 kneeling stance with the front foot elevated on a low step. This keeps guys honest with the weight as they cannot the cheat the weight up by hyperextending their lumbar spine, as by having the front foot up on the step with keep the low back from hyperextending.
Check it out here,