To the OP

Your revelation is simply what experienced riders were doing decades ago, but it's less important now when you have 9 or 10 "speeds" in the back. In the old days, with 5, 6, 7 speeds, you could only make maximum use of your available, usable gears by double shifting across the range (and the best use of that was as a half-step setup plus granny). To initially memorize the steps in the best order, we would calculate all of our gears and make up a little table of them to mount or stick on the handlebar for quick reference as to the proper sequence - and we would shift both front and rear as needed as we moved through the range for whatever the road or wind conditions were in order to maintain the same cadence.

You can still do that, but nowadays, it's not really necessary. You already have so many gears available with each front ring that you can simply use the front to choose the range of gears appropriate for climbing, flat no wind, flat with wind, downhill or whatever. The whole system becomes more like what my motorcross motorcyle had when I was young: A hi and a lo range.

I use a 50-40-30 racing triple now with 9 in back. Gears are so closely-spaced that there is almost never a need to do a double shift to maintain a given cadence unless I also happen to be changing to a higher or lower range for the conditions.

As you ride the same bike more and more, you eventually just know where to go with your gears. For example, often, I just know that I get the gear I want just by shifting the front and keeping the same one at the back. I just do everything instinctively by feel now.

As to triple vs compact double, I don't give a flying frig. I have the gears I want and I passed the stage where I had to impress my friends when I was 8 years old.