Extrasolar terrestrial planets are carbon-poor

Six White Dwarfs with Circumstellar Silicates

The material from the disrupted asteroids orbiting these white dwarfs is poor in carbon, which suggests extrasolar terrestrial planets typically form from carbon-poor material. So much for carbon planets?

Could it be an issue with the availability of carbon materials in the protoplanetary disks of these white dwarfs when they were coming in their main sequence? What are the odds that the initial disks that the disrupted planets formed from had high amounts of carbon like at Beta Pictoris? Surely, the carbon in the Beta Pictoris disk will be incorporated into the planets. If sometime in the distant future, when Beta Pictoris is a white dwarf, will any disrupted planets show carbon in their spectra?