"Go for your best sound right at the beginning of every note."
Making your best sound right at the beginning of the note is dependent on the immediacy of the air. Students must understand that it's not just the quantity but also the quality of the air that needs to be immediate.
The air of a held note that's not changing dynamics needs to be the exact same at the very beginning of the note as it is a beat later. This is pretty easy to achieve in the middle register at a middle dynamic for a decent player.
The challenge comes from being able to do that in all registers at any dynamic level.
And why are the world's best players able to do that with ease?
Through lots and lots of highly focused repetition.
Joe Alessi wasn't born with the ability to play freakishly soft in any register. He simply worked his ass off. It's really not rocket science.
It is also worth noting that it takes significantly more time and effort to obtain skills than it does to maintain skills. I guarantee you Joe has spent less time in the last calendar year practicing his extreme soft playing that he did when he was first acquiring the skill.
To be clear, I bet he spent an awful lot of time maintaining it in the past year. But the amount of time he spent getting that ability in the first place might make your head spin right off.
It is my experience that all musicians believe they are willing to do that kind of work to be able to play that well. But it's also been experience that the number who "are willing" to do that work is way higher than the number who actually do it.