Ohhh no no no no...I agree with your assessment of Malmsteen and Vai...but not at all with Satriani.
Listen to the album Surfin' With The Alien..you can walk away singing his instrumentals...
Here's a live performance of the title track..he plays it note for note as he did on the album....he states a melody line, moves to a bridge with another stated melody line...takes off on a speed run (which again is note for note off the album, meaning, it's written...he's not just running all over the guitar) he then goes back to the stated melody in the beginning of the song...and the same bridge...takes off a bit ...and introduces a new melody as the song ends...goes back and repeats it at the end.
http://youtube.com/watch?v=MjNAeELQ_Z8&search=satriani
I think he's the one of the greatest guitar players I've ever heard...
Always With Me, Always With You...Only runs on the guitar for a short period with a great key change..in the middle of the song...and then back to the melody...
http://youtube.com/watch?v=dqg4XeSbSbw&search=always with me always with you
Love Thing...is as melodic as it gets...He does a little run in the middle but goes right back to restating the melody
http://youtube.com/watch?v=U5r9NP1WMj8&search=satriani
Nah...Satch isn't the same as the other two who NEVER make a melodic statement...
Oh...btw...the kid in the video was great. Thank you.