Apart from Eric Burdon, Chas Chandler’s opening bass lines were a distinctive element in their sound. They caught your attention. Several of their biggest hits featured this: It’s My Life, We Gotta Get Out of This Place, and Bring It On Home To Me come to mind, in addition to I’m Mad Again from their first LP. Also, Chas was a great backup singer who looked good on stage. Alan Price did great, bluesy organ work (e.g., on The Right Time from their first LP), and Hilton Valentine’s arpeggio intro to House of the Rising Sun was imitated by tens of thousands of aspiring guitarists.
Agree with all you mentioned. I was just watching some videos and when the organ player lays into it it really kicks the songs into overdrive.