I've played Anglo for about 12 years now, based on Noel's methodology after attending his workshops several times from the very start of learning the instrument.
I'm a left-side anchor, right side "bow hand" player, with one of the instrument left side corner points on the inside of my left leg.
One enhancement I've made on his left side anchoring, and probably related to that I also play the Uilleann pipes where we use a leather "popping strap" on the leg to seal the bottom of the chanter, is to use a piece of leather on my left leg (about 8" square) to keep the left side from sliding around on my pants. I don't know why everyone doesn't do this. It absolutely keeps the instrument from slipping around and is very comfortable.
With the leather square in place, I can remove my left hand from the instrument and it will not move on a push.
The goal is to absolutely minimize the tension and energy in the left arm that one might waste stabilizing the instrument. I find it allows me greater accuracy and speed on the left side as well.
It's also a lot more comfortable to use the leather if you're wearing shorts. I handed out a bunch of these a few years ago to the other students at Noel's West Coast workshop.
All the rhythm and dynamics are done with my right arm. The only energy in my left arm is stabilizing the instrument on a pull.
I also use my right little finger against the right side (something else I see Noel do at times and that he recommended to me) to provide additional right side stability to insure symmetrical and parallel bellows pushes without rotation about the right side center axis if unstabilized. Without the pinky stabilization, it's very easy to have the top of the bellows tilt in on a push as a result of the right thumb energy against the hand rail while the bottom which is unsupported tilts out. The two motions end up canceling each other out, essentially creating a zero pressure change for a fraction of a second and result in slower and less efficient and precise playing. I spent a lot of time working with Noel on fixing this early defect in my technique. I have some early videos on YouTube of tunes I posted before I fixed this issue in later workshops with Noel, it's almost embarrassing now to watch them, the top tilt on push was so bad.
Additionally, if you watch Noel's playing in detail from many angles, you will also see that he puts a little inside bow in the bellows which provides additional stability and efficiency, along with almost a lifting motion when closing the bellows. Think of a Slinky (i.e. an instrument with very supple bellows). If you hold it straight across with no bend it will just sag and wobble unpredictably when pressed or pulled. Put the tiniest bit of a bow in the arc of the Slinky and now it moves much more predictably and with total control.
I'm a huge advocate for Noel's playing methodology and ergonomics, they absolutely work for me. Everything he does, he does for a reason and, if you ask, he will tell you exactly why. Everything is about control and precision, and having a solid platform and absolutely rock-steady and predictable bellows motion is critical to play quickly and accurately.
Now, could this all be done with right side anchoring? I don't know. Noel's techniques and ergonomic choices work well for me so that's what I advocate and teach.