It’s referred to that way in books on the history of the time, and was also known by that name to 19th century preachers themselves, who ceased going there because it had already been “burned over” and there was nobody left to go to the revivals.
It did leave people with a predisposition to follow individual preachers rather than a church, though, and that was one of the things that contributed to the success of Joseph Smith.
Personally, I think the whole question of Mormon beliefs will eventually be resolved the same way the question of admitting blacks to full membership was resolved: the president of the church will have a dream or a vision telling him to renounce certain things and accept a more orthodox theological and possibly even historical view. There are many people in the Mormon Church who would probably be very happy to hear such a revelation.
I lived in an area with a lot of Mormons, and I can see why it would be very hard for them to think of doing anything else. It was a very complete system that controlled every aspect of their lives, and in addition, if they left or even doubted the Mormon church, they would lose all their friends, their family and the whole structure of their lives. But I suspect this will be resolved in some other way, and then the Mormons will become more like the Mennonites or some other group that also has a very complete way of life and is somewhat separate, but still holds to orthodox Christianity and has that in common with other Christians.
I don't think I'd categorize it as 'success'.