Why are thyristors used in xenon trigger coil circuits?
Your premise is wrong, IGBTs are very common in speedlights and some studio flashes. That allows the flash to be terminated early, leaving charge on the capacitor.  Some IGBTs, such as Toshiba's GT8G131 are specifically designed for strobe applications.
It's not as important in a studio flash where you can charge the capacitor leisurely to a known voltage before discharging it with a thyristor.
Both devices are capable of handling a high pulse current, and withstanding hundreds of volts with a relatively small die size (compared to, say, a MOSFET). The IGBT has the advantage it can be turned off while still conducting substantial current.