Your priority list is different than mine, because this is all subjective based on biased personal opinions. I prioritize based on probability of success, if you rate BTV success rate as 1/5, I would not put it on top.
Anyone can pinch their noses and blow or swallow, there is no barrier for learning Valsalva and Toynbee like ability to control muscles that you did not know otherwise existed.
You can not verify how a student is able to equlize, you just depend on what they say. So, I assume they have no special talent or case and start from most simple to learn: Valsalva and Toynbee. If they can succeed, they can safely try other, more advanced techniques as well. If we start scaremongering Valsalva, we will create an environment where beginners will be worried to do most basic technique, this is potentially more dangerous as we want them to equilize timely and correctly and whichever technique they might be using.
Of course any instructor has different priorities, and I think it is normal that each instructor presents as the first equalization method his "favourite" one, the one he uses everyday.
And this makes sense, because the students will see it being used by their instructor, and it would look strange to them seeing the instructor using something different from what he did teach them...
So I understand that an instructor who uses Valsalva introduces this method as the first one (but followed by the other methods, always - because Valsalva is NOT for everyone, exactly as each of the other methods - we are all slightly different...)
Indeed, Valsalva is not so simple as it appears. Definitely much more complex than BTV.
BTV is the simplest one. You just ask to the student to open the tubes, and, if he can do that, he is done: no need to pinch the nose (which requires to have at least one hand free), nor to synchronise the noise-pinching action with some other voluntary action.
A number of my students had big problems learning Valsalva: this is a method which is really simple for free divers, as their mouth is closed, so blowing sends the air pressure to the nose. You pinch it, the pressure cannot escape, and it forces the tubes to open.
But for a scuba diver, with a reg in his mouth, the airway is usually open (and we insist a lot in keeping always the airways open).
So, when he blows, the air tends to escape form the mouth. For avoiding it, some voluntary control of the valves inside the head is required, raising the tongue and lowering the soft palate, so that they close the path to the mouth.
It is not so simple to control these valves, as you did correctly point out. A (small) number of students cannot do the Valsalva when breathing from a reg (they still can do it without a reg in their mouth, when freediving). Typically those are the students who also have some problems clearing their mask (again, they have no control of the valves, so they cannot force the air to go out form the nose, instead of the mouth).
In my career as no-profit instructor (5 years) plus the following career as a professional instructor (other 5 years) I certified more than 1500 students. My wife did almost the same number.
So, with a total around 2500 cases, we start to have some statistically significant numbers.
Only 1/5 of students can do the BTV, just asking them to do it, with no specific training; but there are at least 1/10 of students who cannot do Valsalva.
In my statistics, another 1/5 of students do the Marcante-Odaglia without any specific training and continuing breathing. It s definitely simpler than Valsalva for a scuba diver with a reg in his mouth.
Many experienced divers are actually using Marcante-Odaglia, but they do not know, and they think of being using Valsalva instead, or perhaps Frenzel.
And another 1/5 do easily the Toynbee.
So 3 over 5 students are better served by methods DIFFERENT than Valsalva. It is OK to teach ALSO Valsalva, but not to ignore the other valid, safe and easier methods, which are the preferred ones by the majority of divers.