For most Americans, the Scottish rock group Simple Minds will always be synonymous with their number one hit from 1985, “Don't You (Forget About Me),” from the John Hughes movie The Breakfast Club.

Simple Minds is most often categorized and marketed as an ’80s new wave group. Yet, that’s very misleading, since this multiplatinum-selling band is about as straightforward rock ‘n’ roll as it gets, ...