Well today I got my answer: YES, it's absolutely necessary to cover the entire roof of panels and Subs with insulation! It was a mere 72-degree day and my roof was too hot to touch from the inside. Panel truck roofs are so large that insulation becomes much more crucial than for pickups. It was sweltering! I guess I'll have to not scrimp on interior insulation....
I have painted the outside of the roof of my '57 Suburban white: it makes an amazing difference in temperature inside: Parked in the sun, it used to be that I could not touch the roof inside it was so hot; now it just gets lukewarm. I knew the theory (white reflects heat) but experiencing it was an eye-opener!
It seems the OP was talking about noise though, and yes, the roof of my Suburban is like a big drum: something I thought would help (but never got around to doing) would be to "stuff" something (rubber?...) between the roof skin and the roof crossmembers to prevent the skin from "flapping" and making noise.
My Suburban, which is usually parked outside, gets a lot of condensation inside the roof, so something that does not react to humidity (or soaks it up) is a must.