Well, your word “springboard” is a key. The singer believes that the little catapulting action from below will yield a more exciting upper note. And, if the elastic tensions are in good balance, he is sometimes right. Possibly I can offer an example or two from my own far-from-starry singing experience, using spots where there are written acciaccature. I’m a baritone, so I have never spent as much time above E or F as a tenor of any developed type, and my first example doesn’t even quite get across the break. But it does jump a full octave, between E-flats. It occurs in King Gama’s song in Princess Ida, which rattles right along with lots of wordplay, and I was happily aware that striking the crush-note cleanly and vaulting straight to the upper note gave the latter a zing it wouldn’t otherwise have had, besides kicking the rhythm onwards smartly. The second, very different, example is from the end of Barnaba’s “O monumento” in La Gioconda, which I never sang publically but worked on in coaching sessions. After coming down from the F on the penultimate phrase (“E tu la BOC-ca,)” one has time for a little catch breath before launching back up to the G on”PAR-la!” The best Barnaba I have seen, Leonard Warren, ignored the lower acciaccatura  and attacked right on the G, with strong lip compression. It worked for him. But I found that finding an open “a” and striking quickly off the acciaccatura up to the G, while gathering the vowel, got the best result for me. So maybe Ponchielli knew something about what would get the best effect at the end of the monologue, and perhaps it was the same thing that some of our tenors, stylistic paradigms or not, also know about their own voices.

Next, you make two assertions which, if I understand them correctly, I find suspect. You mention a humming exercise as a test, and then speak of diminishing the tone and softening the support as the voice ascends. This humming idea (and I gather yours takes the form of a glissando, or “siren,” up and down the range?) has become quite popular in recent years, and I’ve often spoken with other teachers, coaches, and students about its supposed utility, and heard it demonstrated in various patterns. I think it’s as useless as the inescapable “lip trill.” It’s just a cosmetic trick, which I’m sure Jonas Kaufmann, and any number of singers far less advanced than he, could easily demonstrate for you if asked. What is the use of detaching the sound from vowel formation, from the necessity of engaging the support system with a resonated tone as the goal, and then pretending you’ve negotiated the registers? I understand the potential of a hum as a therapeutic device, as an early step in recovery from vocal abuse, but I don’t think it’s any test of functionality in the sense we are debating. And do you really mean your thought about diminishing and softening support while ascending to be a general statement? I think that while the problem of diminishing the tone when approaching any pitch area that is tending to bulge is an excellent one to pose in particular cases (though it is crucial to sustain support, not weaken it!), and that it’s good to be able to do it, I don’t see the value of it as a habitual way of climbing through the range.