Yes, you could convert the basalt into glass. But basalt fibers have some real advantages over glass fibers, mentioned in the linked page:
> Basalt Woven Textile has high corrosive and chemical resistance to the influence of a corrosive media: salt solutions, acid solutions and particularly alkali liquids. The specific strength of basalt fiber exceeds the strength of alloyed steel by a factor of 2,5 and the strength of glass fiber by a factor of 1,5. Heat-insulating items made from basalt fiber combined with inorganic binding agents may be used by temperatures up to 700°С. In addition there is a range of compositions consisting of basalt rocks that have a higher thermal stability – up to 800°С.
> Basalt Woven Textile has high corrosive and chemical resistance to the influence of a corrosive media: salt solutions, acid solutions and particularly alkali liquids. The specific strength of basalt fiber exceeds the strength of alloyed steel by a factor of 2,5 and the strength of glass fiber by a factor of 1,5. Heat-insulating items made from basalt fiber combined with inorganic binding agents may be used by temperatures up to 700°С. In addition there is a range of compositions consisting of basalt rocks that have a higher thermal stability – up to 800°С.