I would disagree, I think they are becoming more popular as they are becoming better made and made with a more modern seat as opposed to the old 'stockmans seat' with your feet out in front of you!
As Xivo said, they were made for stockmen who were riding all day out in harsh terrain. Nice deep seat to be comfortable, and the knee rolls give you security for different situations - Wether it be galloping down a rocky, hole covered hill, or turning hard and fast with a cow.
Nowadays they are used as working saddle for stockmen still - And are also the saddle of choice for campdrafting and polocrosse, both very Australian sports. They are also the traditional saddle used on Australian Stock Horses - and is what the majority of ASH horses are shown in.
NO AUTHENTIC AUSTRALIAN STOCK SADDLE HAS A HORN. A horn is something that has been tacked on simply to appeal to the US market - Stockmen didn't rope calves off horses, they used transportable yards and a crush to doctor cows. A horn gets in the way of your body when campdrafting/fast stockwork out on the plains, as the traditional seat for a stockmen in fast work is a very forward, hunched seat.
Most stock saddles in the US are cheap, poor quality and badly balanced. A good quality Australian Stock Saddle is a thing of beauty and comfort... The market for custom made stock saddles is roaring in Australia - Some makers have up to a 2 year waiting list. I recently bought my own custom made stock saddle for my ASH - And I have sat in nothing that compares to it comfort wise, and it is the only saddle my horse has been comfortable in so far.
If you have a chance to, have a sit/ride in a true Australian stock saddle - Syd Hills are a better known brand but not the best. Names such as Mackellars, Coopers, Jacksons, Peter Nelsons, etc. are sinonimous with the better quality stock saddles you can get today, and many actually increase in value with age and good care. If you are interested, you can look in my archive of threads I have made and I have posted pictures of my saddle.