Well, strictly speaking, you CAN turn a rock into glass, but the rock is made of many different minerals which each have their own particularly melting/freezing/crystallization temps that makes the solution (which is what a magma is, a solution in a SiO2-dominant liquid). Using quartz gives a fairly pure solution (SiO2 liquid) which tends to not have the many crystal formation and inhomogeneity problems that happen from very impure liquids. Also, quartz is transparent to visible light so useful as glass.
It is like trying to freeze salty water compared to pure water. The secondary materials cause lots of problems for making whatever the person wants. A little sodium borate is nice as an additive, say, or a bit of lead, which can help lower melting temps and make the glass easier to work with (pure silica glass is a real bear to work with, very viscous and has to be really hot because quartz/SiO2 has a very high melting temperature).
In effect, all magma, lava, is melted rock, and if you look around at what happens in nature, you will find that most of that melted stuff does no make a nice and useful glass. All those other elements muck up the works, so to speak.
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