The whole idea is to match revs between the engine and transmission. Double clutching can accomplish this, as can heel-toe shifting. IMHO, two different approaches to the same goal.
Some may scoff at this, but I've worked hard to at least be
able to shift any of my cars without the clutch. All you do is, while driving in a straight line, with little or no traffic, try to downshift by raising the revs with the throttle while
gently pushing the gearshift into the next lower gear. When (if) you have the revs exactly right, the car will snick cleanly into the lower gear.
Once you are able to do this at least some of the time, you will understand the reasons for double clutching or heel-toe shifting.
This has great benefits on the track, as you will be able to downshift before, (or in) a corner, without the car shuddering, bucking, bogging, or the like, depending on speed and gear selection. My goal in shifting is to be able to shift without a passenger even knowing I shifted, except for the change in engine RPMs.
BTW, this is great for extending the life of your clutch. And, there is nothing wrong with shifting slowly and cleanly. I never understood the guys who bang the car from gear to gear. I shift with my fingertips, not my fist.
Jim