It seems like duct tape is really temporary fix for everything.
Obviously (or not) is is not meant for ducts.
Main questions:
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.
What is duct tape's actual purpose?
In the past, sheet metal workers used it to seal the joints on their metal ductwork.
Hence the real name "Duct" tape.
Then a company created a brand name from the bastardized name called "Duck Tape".
When should I use it for a permanent fix?
Probably never. It may survive for decades buried in the insulation in your attic. It dries out and crumbles in just a few years in most environments. If you leave it outside exposed to the weather though it disintigrates in a few months. Sheet metal workers use fiberglass reinforced reflective tape to seal duct joints now.
Is it really a product with no intended purpose other than for people to be creative in DIY and repair?
No, it is just fairly inexpensive and handy in many cases. 1001 uses!
In addition to other good answers already, take a look at tape meant for actual duct work nowadays. It is more metallic than the duct tape you probably have in mind, which is really more like Gorilla (brand) tape or gaffer tape as others mentioned.
Ironically, the metallic tape that I use on duct work is far less all-purpose than the Duck (brand) tape you probably have in mind. I wouldn't put Duck tape on my ducts but I would do hundreds of other repairs and survival tricks with it.
