Is ok to have an air duct that is just insulation?

No. You want the duct's interior surface to be smooth, preferably. If you have to have flexible duct, your best bet is to have it installed such that it is mostly taut all the way back to the unit, well suspended over its entire length to prevent kinks, and insulated. You should not have bare insulation showing inside your duct, or worse - bare insulation BEING your duct. I recommend you get in there and replace the damaged portion, or replace that half-wit kludge job with the correct material.

modern air ducts are a foil over insulation, whether it's rigid board type or soft type. You should not have one that's ONLY insulation, without the metallic covering.

Almost every plenum has insulation glued inside the sheet metal. Some plenums and ducts are completely made of insulation without metal. Almost all commercial duct work is the same, metal with insulation inside.

I retired some years ago so I don't remember the trade-name for it but in new residential construction A/C Duct is commonly fabricated with lightweight compressed Fiberglas duct making material that's covered with a thin layer of metallic Kevlar & simply connected with metallic or nylon duct tape,,,

Cheaper than Metal Duct it looks allot like fiberglass insulation inside, but to my understanding there isn't any issues with it,,,

"FIBROUS GLASS DUCT" is legal when installed correctly.

it's ok. adds some extra drag which was compensated for with slightly larger size

Insulation being fiberglass should not be the conduit. It would seems some of the fibers will constantly be circulated thru your air vents causing breathing problems. The ducts should be metal and free of fiber.