Front leg action

I'm not a pitching coach or guru, but I'll give you my amateur thoughts on it.  I don't really think it matters too much which style you use, as long as your style does not cause you to open your hips too early in the delivery.  The swinging front leg can also cause momentum to carry you towards the glove side instead of keeping all your momentum going towards the plate.  Ultimately, that's what you want - all your weight and energy going towards home plate, not toward first or third base (depending on righty or lefty).  

In terms of front leg landing, I like a soft land, but firm up as your arm comes thru.  If you land too hard, it can cause a jolt which can effect mechanics.  If you land soft and stay soft, you will not get all the forward energy transfer you gain by firming up.

Hope that makes sense.

Front leg action is typically a result of how you come out of leg lift & hand break...for the most part all pitching movement patterns are dictated by the previous movement....same with "soft" vs. "hard" landing.  As for quiet lower half, fast upper half...not sure where that comes from, but IMO - NO. 

Very much like hitting, there are many "old" school verbal cues that quite simply are garbage...someone heard somebody say it, so they repeat it, really not knowing what the heck that is supposed to mean.

Hitting & pitching are very similar, as it relates to power / speed production.  The largest group of muscles related to bat speed (hitting) & arm speed (pitching) are the larger muscles of the core (from the mid thigh to the core muscles in the abdomen)...this is what creates bat speed or arm speed when activated / utilized properly.  Upper torso throwers are called "arm throwers", which is not desired.  Be careful what you think you may see when comparing different MLB pitchers as you described....the ones you describe all utilize their core to develop arm speed...since they have different styles of how they activate their hips, their front leg action looks different.  Front leg action should for the most part be a function of how they go into hip rotation (back hip rotation), which occurs just prior to front foot strike.  Those who generate more speed into landing will typically have an appearance of a more "hard" landing, while those who generate less momentum into landing will appear to have a "soft" landing. 

There are other factors regarding velocity (or pitching in general) other than how they activate hip rotation, such as arm action, genetic flexibility, strength, decelerator muscles, and training (arm care & recovery).

The two simple things to teach that are good starting points are to drive your heel to the target and land soft. Both of these things are used simply in order to get the rest of the delivery to be more effective.

Driving your heel to your target helps make sure your entire momentum is headed in the right direction. 

Landing soft helps make sure your hips and core can be explosive. If you land hard, that means your weight has leaked forward instead of stayed back and fired through on rotation.