I own & show Koms. My dogs are finished champions. I am a long time member of the Komondor Club of America and have been involved in the show world for many years. My B**** was accepted to be bred to the number one Komondor in the country. My breeders and mentors have been in Koms for over 30 years and are both AKC judges certified in dogs across many groups.
First of all, the Komondor is part of the Working group, not the herding group. The Puli is part of the herding group. The Komondor is a dog that
does not like to run and play. It has little or no herding instinct at all. If you want a dog to fetch a frisbee, the Komondor is absolutely the wrong dog for you

It has been bred for ages for the sole purpose of guarding flocks. It is a Livestock Guardian Dog, not a herding dog. So, it was bred to lay with the sheep and guard. It is very quick and agile, (mine can leap over our couch without a problem), but it is a reserved dog, focused on business and not play. It's main job is to lay around watching (guarding) its family and it does it very well
You are correct in that the Komondor is not a good dog for beginners, although it is one of the best family dogs around. It is wonderful with kids because its kids, its family and other pets becomes its "flock." It will protect its flock with a vengeance. It also has been bred to be an independent thinker, to make decisions on its own when it is out on the Putza with its flock. Which is why you don't see a whole lot of Koms excelling in the obedience arena. Also, which is why the dog is not a good choice for a beginning dog owner. With the strong guardian instinct and independent thinking, the dog has to be well socialized, extremely well trained, and a gentle but firm hand must be maintained at all times. Otherwise you could potentially have a dog that is making the family decisions on its own. Never a good thing with a guard dog.
Actually, Komondor puppies are born creamy white and fluffy. They look like little cotton balls. You are correct in that starting at about 9 months, the coat does become kinkier and starts to cord. You have to separate the mats into cords. This is a process that takes until about 18 months of age. If you are not diligent in separating those mats into cords, you will have a dog that is one huge mat. Cords are really just controlled matting. By the way, other dogs with similar coats can also be corded. Poodles are one of them. You have pretty sore hands for about 9 months. After that, a once daily maintenance of checking cords is all that is needed, because as the coat grows, the new hair (yes hair, not fur), grows in, it can mat too. But since the cords are already established, this is easy. You just grab the two cords and pull apart to the skin.
No, No, No! You NEVER, EVER brush out a corded Kom. First of all, it is impossible to do. You cannot undo the cords. They are so tightly wound, it would be impossible. You would have to shave the dog and then brush. Once brushed out, you cannot just "re-cord" the coat. It is a long, long (see above - takes about 9 months) process to cord the dog.
The dogs you see at Westminster and the big shows have been cording for several years. The dogs with coats close to the ground are at least 5 years old and have never been shaved or brushed. That is why show people are so anal about coats. We actually tie up the long cords to minimize breakage - because once damaged, that is it.
To properly bath a Komondor, you use a high powered nozzle on a hose. We place our dogs in a full bathtub in order to get water to soak into the cords. Then we lift handfuls of cords up away from the skin and blast with garden type sprayer. You are blasting all the little seeds, dirt and other stuff that becomes imbedded in the coat. You never use bluing or conditioner on a corded coat - the bluing will stay in the coat and you will have a silver dog and the conditioner makes the dog greasy.
True. You are correct in that you need to properly dry the dog otherwise it will mildew.
So, you take your wet dog - which is holding as much water as a large string mop, and proceed to wring out each cord. You then place the dog in a crate with lots of towels and lots of fans, changing the towels frequently. The dog will usually dry in about 24 hours, depending on humidity and how thick the coat is.
For my 7 year old male that has cords dragging on the ground - it takes me about 1.5 hours to wash, 1 hour to wring out the cords and 24 hours to dry. I have bathed the dogs the day before a show and the next day, I have had them still wet, particularly on their chest.
Enough about the kom.
But please, please make sure of your info before you impart it to this board. You are saying you are an expert, so please make sure your info is correct.