Some techniques in hapkido are practiced with a foot sliding along the ground or remaining in contact with the ground. For example, in a sequence we call a stepping pattern, it isn't uncommon to step with one foot moving forward, and then slide the back leg into position. Similarly when practicing sweeps there are several sweeps where the leg is picked up, but there are multiple others where you slide your foot along the ground until just before you make contact.
The justifications given here are related to stability and "getting power from the ground."
When I practiced rapier fighting, however, the emphasis was always on picking up the feet. The justification given for this was that you weren't always sure what the terrain would be that you were fighting on, and you wanted to pick up your feet so as to firmly place them where you wanted them. We also tend to practice hapkido barefoot and inside, where we tend to practice rapier with boots on and outside.
I've seen this now in a few other places: Either the foot is never supposed to slide across the ground, or it consistently does in some situations.
What are the pros and cons of doing this? Is it just practiced as an artifact of the arts being indoors on good mats or do you actually generate stability/power/flow by remaining in contact with the ground for longer?