I wonder if diamonds become cheap enough, and we are growing the crystal anyway, if we can introduce dopants and get interesting electrical properties.
Other wide bandgap semiconductors, i.e. silicon carbide (a.k.a. "moissanite" in jewelry) and gallium nitride are well on their way to make silicon completely obsolete for power semiconductor devices, but they are still many years away from reaching their full potential, in good part because their crystals have still too many defects in comparison with the crystals that can be grown from silicon. Because of too many crystal defects, for now the only commercial SiC devices are MOSFETs and Schottky diodes, despite the fact that SiC thyristors have exceptional properties for working with very high voltages, but bipolar semiconductor devices are much more sensitive to crystal defects, so their mass production is waiting for improvements in crystal growing.
Besides SiC and GaN, there are a few other semiconductors that have greater chances than diamond to become useful for semiconductor devices, e.g. gallium oxide or the sulfides of molybdenum and tungsten.
In diamond, there is not only the problem of crystal defects, but also the currently known dopants have various undesirable properties, like becoming active only at high temperatures, so some diamond electronic devices could be made to work in an oven or on the Venus surface, but not at room temperature.
While the use of diamond as a semiconductor is far in the future and there is no certainty that it will ever become able to replace silicon carbide, if artificial diamonds become cheap enough they might be used much more frequently for heatsinks, including in computers, as the material with the best thermal conductivity.
Diamond heatsinks are already in use, but only in niche applications where price is irrelevant.