It's not an analysis, but a series of observations follow.
I presume that the crunch sound is of ice yielding. The blade is wedging the ice away from it's original location. The stronger the push, the deeper the groove left behind. The displaced ice is the source of snow on the surface.
From an energy standpoint, the sound produced as well as the non-elastic deformation of the ice must reduce power available to the skater. That's engineering dynamics. Anecdotally I can skate with the most perceived speed and power a few minutes after an ice cut. The somewhat softer ice is quieter and my blade doesn't slip with a strong push. I feel faster and in better control. Harder ice seems to produce more noise from pushes, and my blades slip sideways more. Larger amounts of slip become disconcerting, especially when my blades are loaded with cornering forces in addition to stroking pushes. That's the limit.
Hockey players can really tear up the ice during strong cornering accompanied by a great racket. The ice damage is very visible and is one cause of a figure skater's lament.
BTW, have you ever heard a high-pitched "screeeee" when your blade placement on the ice is too flat? The blade skidding is huge, and you're close to a fall. Thankfully, I don't hear that sound very often.
Anyway, those were a few thoughts that came about your questions.