All you need to know about Cocker is that he put out a version of "I Shall Be Released" around the same time Dylan and the Band put out their versions and it stood up. It's hard to imagine somebody putting out covers of contemporary music today and being well received.
His 80s stuff is forever destined to be underrated. Most people who love slick 80s sounds don't want a gruff rock singer. And most people who love singers like Cocker wouldn't be caught dead listening to anything 80s. Alas.