Varanger,
The problem with vx is the wing is asking for more air please. Maneuvering is out of the question, we would stall. Read Stick and Rudder by Wolfgang Langewiesche. His principals are what most of the guys that have chimed in here start with, regardless of their technique. Wolfgang uses the word "zoom," which expand to zoom reserve airspeed. It is enough airspeed (the wing likes more than just enough to hang on) allow temporary climb and maneuvering without the engine. Read about the law of the roller coaster. The numbers you were given in PPL ground school were all high altitude orientation. Yes if we are high enough to recover from stall and even spin, altitude and not airspeed is preferred. Altitude is time. In low altitude orientation, however, airspeed and not altitude is life. If we lose concentration, lose and engine, almost hit terrain or an aircraft, hit sheer or gust spread, or whatever at Vx we have little airspeed to work with. Vy is chosen mathematically. It also gives the wing little to work with after three seconds startle at Vy pitch attitude, not necessarily Vy speed. I haven't had many engine failures on takeoff, only one. I was still level in low ground effect, my default until zoom reserve airspeed, and I simply landed on the runway remaining. On nine of the other twelve, they were six second deals from total loss of power to touchdown. On takeoff, this is what you have. You mentioned best glide speed. Who cares, I want to maneuver to that survivable landing zone in the near hemisphere. Different airplanes? Sure. In a Piper you probably just have time to switch tanks. My student was able to in a Cub once. I was already committed to a fine landing in the adjoining field. I had taken the controls and I elected to land. Low and slow is a no no. I spent 17,000 hours at 200' or lower and my wing wanted all the energy I could provide. A quarter mile from the end of a spray run in a Pawnee, I went full throttle on that 235 hp tiger. I did not want to be slow coming out of the field, nor do I want to be slow coming out of a perfectly good airport with another thousand feet of free low ground effect energy in front of me. The Savage stalls when you need to maneuver to miss terrain and you don't have the energy. It stalls a lot slower than 34 kts in one inch ground effect on every landing. Rounding out and floating doesn't make it quit flying faster. Yes, at Vy of 65 kts, you have more margin than most airplanes. Don't abuse it. Learn energy management. Learn to fly the wing. With two big boys at Monte Vista, Colorado, where I instructed in an 85 hp C-140, also with a pretty good margin, using that long runway to get to 80 kts in low ground effect was a lot safer than 65 kts. No, you will seldom need that extra ground effect energy. And then you will.
I'm an outlier here, but I don't teach students to stall in the pattern when startled. I teach what Wolfgang suggests, "what does the airplane want to do? So what does the airplane want to do, what will it always do, why can it not stall itself? When does it want to get the nose down to save the wing? Why are we fighting it? My students muscle memory is to not pull without zoom reserve airspeed and not to pull in turns. It doesn't upset the airplane, only the DPE, if we allow the nose to go down in turns and then return to what we were doing before the turn. Not much lost to save ones self, muscle memory wise, is a startle situation.
You are asking, and that is good. There are lots of answers out there in aviation. Test the spirits, the Apostle Paul advised. You have a brain that surpasses the most powerful computer and you have the hands and feet Rob mentioned that are super sensitive if you listen to them. You are on you way and the only way we old farts can look good is if you pick up some of their valuable techniques. Have fun, pay attention to the airplane and the old farts.
I really don't understand how they avoided it for so long 