I often mentioned that the best guitarist I have ever seen live was a local guy who had a cheap Squier strat and small transistor amp, kind of like the 30 watt transistor amp in the Satch video, and he burned everything up.
Whenever people, usually inferior guitarists with better gear, criticized his cheapo gear, you only had to walk into his home and see his gold records on the wall. 'nuff said and that pretty much shuts up any detractors of his cheap Squier.
It's his way of saying f-you to all the gearhounds out there with no talent. He lets his guitar speak for him and he finds no need to burn down medieval churches to bring attention to his music.
Even though he had a huge ego, and wasn't the type of guy to argue with (think Lars Ulrich), he also recorded local bands and helped many get it done and get it on the air as should be the ultimate task.
His bare bones setup with small amp and Squier got the job done, minimally, and then he could spend the rest of his time wringing out perfect lead, perfect chorus, and correct harmonies, if needed. You only have so many hours in a day, and then you have to learn numerous songs as a studio guitarist and keep the future booked, not to mention sound recording clients.
He made sure not to over-record and kill a feeling of any song/passage, yet he made sure the basic track was good enough for the job. He knew the difference between tight and sterile and thus the work he got as a studio guitarist and now recording engineer.
I remember the first time I saw him in a coffee house and he sang backup sans mic and got every type of sound out of his strat and it all sounded professionally mixed by a good board operator but it was really just him and his guitar. Distortion, gain, and clean were all the same controlled by just his strat's volume knob and he never overplayed a single note.
When I see the Satch video, I see a master utilizing what gear is there to the absolute maximum and that translates into a good guitar sound, and yes, gold (or better) records on the wall at home. Anybody can find a perfect Satch concert video where he has the control of what gear is there and how the monitors/speakers are set up for any given concert hall, but what Satch does on a guitar that is not his, some effects and a small amp is just genius.
I used to think Kirk Hammett (a Satriani student just like Steve Vai) was overrated but then I saw some stuff he does just with small practice amp tooling around and the guy practically never hits any bad notes and can make a basic backstage setup sound like a finished recorded product. I think he got that from Satch and from what few leaks came out about Satch and his rigorous teaching techniques, it was to pay homage to the song, and nothing else. I remember Vai talking about hiding when he saw Satch on the street when he didn't practice his lessons.