It's fascinating to me because everything Miller says is actually pretty obvious. However, it's easier said than done. Many things in our world are obvious, and yet how many of us ignore the obvious every day for our entire lives? (For example: I want to lose weight= diet and exercise...so obvious, and yet how many of us don't do it? And the list goes on and on....) I wish I had more chances to work with students on comping, and I mean beyond the nuts and bolts of form and voicings. That stuff is important as well. But beyond that, much of it is philosophical.
Mulgrew Miller is one of the best examples of legendary-musician-turned-jazz-educator. Because of his vast experience, everything he says comes from the real world of jazz. It's not merely theoretical. My inclination is that comping has to be developed by playing with people. It's interesting that Miller is saying that you should actually practice it abstractly-on your own- before you get to the gig. I think this makes a ton of sense. The idea is that you should have a base of "laying it down" so that it swings, or whatever you are trying to do, and it "feels good". I think having a good "feel", whether comping or soloing, is one of the most important things you should have as a jazz musician. This might mean the difference between work and no work. I believe that my initial success as a pianist was not because of my technique( I had little) or repertoire( I had even less). It was because I had a knack for making it "feel" like jazz.
The big question is, HOW do you make it feel good? Well, for starters, listen to the great compers: Wynton Kelly, Red Garland, Bill Evans, Herbie Hancock, McCoy Tyner, Kenny Kirkland, Mulgrew Miller, Hank Jones, Tommy Flanagan, Cedar Walton, Horace Silver. Listen to how they provide harmony and create rhythm, and where do they leave space and how do they fill in the spaces. How do they help the soloist without getting in the way. Maybe play along with them on recordings.
The next step is to find what works for you. And that depends on your taste, and it also depends on who your are playing with. Some people want, or may actually NEED, for you to lay it down in a strong way. Others might want you to play very little. Some maybe not at all. Piano can be omnipresent or superfluous, or everything in between. It's a constant journey to find the right balance. It's a combination of trying to read the mind of the soloist, and "make them feel comfortable", as Professor Miller said, and using your own judgement.
I remember when I realized how important comping is to a pianist's career. I went down from Baltimore to Washington D.C. to sit in with saxophonist Paul Carr at a club called Takoma Station. I sat in on a rhythm changes tune. I guess I was in a listening mood, because I felt I should listen before I played. Carr played a lot of notes, but when he left a space, I played one chord, let it ring, and then listened again. I barely comped at all. Carr came up to me after the tune and exclaimed, "Wow, I LOVE your comping!" He then hired me for a bunch of gigs. Well, they say "less is more." But you have to figure it out for yourself. I'm still trying to figure it out as well. That's the great thing about this music; you are never done learning.