What i understand from the people smarter than me (i.e. the exercise physiologists :)) is that Vo2max is useful because it is a measurable proxy for the amount of energy you create aerobically (which cannot easily be directly measured) and isolate it from other processes. If oxygen usage is higher, then all else equal, more energy is being made aerobically.
The upshot of this is that any aerobic training, as long as it’s enough to stress your body into adaptation, increases Vo2max: threshold intervals do, tempo does, even LSD does. That said, from what i remember the research has shown that intense aerobic intervals drive more of these adaptations, but require more recovery (of course).
So if this is true, then i’m not entirely sure why short and intense intervals are the ones traditionally called “Vo2max.” One guess is that they are called that becuase they are at a power that will eventually elicit vo2max, and it’s in that case really more a description of the power rather than a claim that it’s the exclusive way to get the adaptation.
another reason might be the specificity principle, i.e. that you train at that power and duration to raise that power and extend that duration. It would be a bit of a misnomer though because i believe a (relatively) substantial portion of your e.g. max 3 min power comes from anaerobic contribution, if you come into it fresh and rest fully between efforts. And again it suggests that it’s the only way to raise Vo2max whereas really it’s not. According to Sebastian Weber it’s not even necessarily teh best way (he says that longer threshold intervals actually have more of an impact)
so, long story short there are a lot of ways to skin this cat. Very short intervals can raise vo2max if you do them tabata-style, i.e., with very short rests. At first anaerobic will be contributing to your efforts, but as you go through the short interval sessions it will eventually tap out and the rest will be intense aerobic.
Longer (but still short) intervals can also work to do the same thing. My view is you go for the highest power where you can still complete the session. But if you rest a lot between these intervals you will be getting anerobic contribution as well, and you’ll need to burn that out before you start accumulating the intensive aerobic work you need.
But remember you might need to be fresher coming into these sessions. i.e. to get the power high enough to justify the short duration.