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Almost the half of these costs can be traced back to the two-step heat treatment (stabilization and carbonization) of the carbonaceous precursor fibers (mostly out of polyacrylonitrile, PAN) into carbon fibers. This is due to the long duration in the furnace (up to two hours) as well as the high energy costs (temperatures up to 1,500 °C), which are necessary for the heat treatment.
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It appears you are correct. Compare the energy required to melting basalt at similar temperatures and extruding it through a die — one quick step to IMHO a superior product.