Why the vertical difference between the right-most point of TT and the left-most (union with ST) is not part of a geometry chart? One of the things I often look to determine whether a bike fits a specific purpose is that distance mentioned in the title, that is, if you draw a line from the stem to the seat tube, and then you draw a vertical line from the union of both ST and TT to that line, measure such difference.

Maybe it does not provide any meaningful insights, but IMO, when I see a bike with a higher distance at this "metric", it tends to be more focused in AM / Trail, whereas if this distance is shorter, it's often more suitable for XC.
That dimension by itself hints at a bunch of different things without telling the full story on any of them. It has implications for how much dropper travel can be run for a given seat height, but you can't figure it out exactly without knowing where the seat tube actually ends. It has implications for how much bar height you can or are forced to have, but again doesn't tell you exactly without a measure of how far the head tube extends above the TT intersection. The top of the head tube can get pushed up to accommodate a given fork travel, but you still need to know what fork axle-to-crown dimension is actually intended.