My 11 year old son is diagnosed with AS. For the first three years of his life, we knew he was "different", but so far they were only good differences--except for some sleep problems. He clearly had a unique way of looking at the world, and way, by far, the most fascinating person I had ever known. At about age 3, other things started creeping in, like odd social problems (which I saw as problems with the neighbor kids, being an undiagnosed aspie myself), obsessive rigidness, and anxieties.
Now, he's still a fascinating, wonderful person, and I wouldn't want to change him. However, I would like to be able to relieve him of the burdens that his AS puts on him. He suffers a lot from sensory issues, and has a lot of anxiety about things that other kids don't have anxiety about. He has some self-imposed "rules" that limit him quite a bit.
If curing him means taking away the anxiety, and allowing him to suddenly be able to navigate social situations, and to be free of the sensory issues, then I suppose yes, I would want to do that. If curing him means changing his brain so that it doesn't think in that unique way that makes him so interesting and special, then no, I would not want to do that.