Steve Vai uses mostly a tonal dialect (similar to 20th century classical: a hybrid) so he can slow down much more than Satriani and Petrucci that use modal dialects.
Have you ever heard about battles between rock and metal guitarists?
Why are these guys so obsessed with speed?
Between metalheads you will find rankings about the fastest guitar players ever. Usually an invitation to take part to a G3 tour is the coronation of the career for the modern guitar hero.
Well most rock and metal guitar heroes are Pink.
Aqua guitar heroes in pop/rock are few (Santana, Steve Vai, sometimes Clapton, Brian May, George Harrison, Jason Becker).
Well let's forget about Jason Becker, the ill-fated new-born Paganini: these Aqua guitar heroes are often slow. I don't want to say they can't do fast sixteenth or whatever, they just tend to compose slow tunes.
Eric Clapton is worldwide famous as "slow hand".
Well you know (I hope you experienced once in a life) that Aqua music is the strongest ever if you use "emotions" to rate music. The reason why is that changing chords (Aqua = tonal language or similar) can be very fast. You can store a lot of information in a small amount of time using harmony (or dissonance).
You can store few information in the same amount of time using modal language or minimalism.
So you have two ways of increasing the amount of emotions (and information) in Pink music:
1) a lot of layers, like in Italian Renaissance (5 voices? 10 voices?, 16 voices?) or in dense poly-rhythmic music like Trout mask replica, King Crimson, Dream theater
2) running your scales the faster you can, so you can change them during soloing a lot of times
I am not an advocate of muscular stupid exhibition of speed without any meaning but in some genres a faster guitarist can be useful.
Pink = modal space composing and improvising
Aqua = tonal space composing and improvising (or balanced hybrid).