What is duct tape's actual purpose?
It was meant for ducts.  It's just been obsoleted by better products.

I mean for ducts. 

However it was never the best at the "all purpose tape thing" people currently do with it.  That honor goes to gaffer tape. 

Gaffers are lighting electricians in theater, film, TV and electronic news gathering.  Gaffer tape is to affix cables and lights temporarily to finished surfaces, without marring or gumming the finished surface.  When you see a TV shoot in some CEO's beautiful office, and there's enough light in that office to shoot, it's because gaffer tape is holding some mini lights to the walls in the right places, and their electrical cables are taped down to the carpet.  Can you imagine taping cable down to carpet with duct tape?  And when the shoot's over, all that tape comes up with no mess. 

When you reach for duct tape, what you really want is gaffer tape.  Gaffer tape is not cheap, maybe $15/roll for the lesser and $25/roll for the better stuff.