"Why would non- folkies know 'The Last thing on my mind'?
Was it ever a hit? How often would the song be played on any tv/radio show?"

Maybe they listened to country radio in 1967 when Dolly Parton and Porter Wagoner's version hit #6 on the charts?

The song's wikipedia page lists over 40 cover versions, from Harry Belafonte's to one in German, including crossover folkies like Joan Baez and Judy Collins, as well as country and pop singers John Denver, Neil Diamond, Glenn Campbell, Graham Parsons, Willy Nelson, Johnny Cash, and Pat Boone.

I never much cared for it myself, but I heard that Doc Watson loved it, and not to take anything away from the zoo song, it was liked by a good variety of popular/talented singers and presumably their fans.