In the book, after the diadem is destroyed by Fiendfyre caused by Crabbe, Hermione mentioned that she had read that this fire could destroy Horcruxes. Still, it was difficult to control. In The Order of Phoenix, Voldemort uses that kind of magic against Dumbledore, but Dumbledore repels it. Also it is mentioned in the book that there are ways to stop it. So, why bother and looking for a sword and not using this spell ? Also why didn't Dumbledore use this spell to destroy the Horcrux, but instead got his hand injured?
Inexperienced casters will be able to conjure the flames but will have virtually no control over the curse once it has been unleashed, thereby making the fire a deadly backfire. More experienced casters, such as Lord Voldemort, may control the flaming beasts they create, even condensing it into a single, colossal animal of their desire. There is also a charm to cease the flames as well as one to disperse them, but unfortunately Vincent Crabbe never paid attention in class long enough to learn it, therefore costing him his life. It is also possible that the fire may eventually burn off on its own, if it is unable to consume enough material to sustain it, and if so, the ash left behind may become Ashwinders.
-From the Harry Potter Wiki article on Fiendfyre