Sammy is one of those very versatile musicians that can adapt to different styles, but also understands the expectations of the people he's working with.
People keep forgetting or don't realise that people that work in the field of Arts & Culture & Entertainment are intelligent and talented. Iggy Pop ( James Newell Osterberg, Jr.) came Dux of his school. That's #1.
Stewart Copeland the Drummer & Sting's pugilist partner in The Police is a genius mathematician.
Mark Knopfler worked first as a reporter and farm hand and later as an English teacher.
Don't be fooled by the dopey ones either, it's all an act.
John Lydon ( Rotten ) from The *** Pistols is one of the smartest and quick witted people on the Planet.
The short answer is - Musicians and Actors are intelligent
In regards to Van Halen, Sammy brought a great voice and very importantly, a 2nd Guitar.
Bands with 2 Guitars have a richer and fuller sound.
Sammy wasn't a Show Pony like David Lee Roth, even though I love Diamond Dave.
Sammy was a Blue Collar Worker.
The 5150 album was great because of Sammy Hagar.