Yeah, IGBTs are right out -- they're made to harness the best of both BJTs and MOSFETs, specifically for switching applications. The current density is massive, many times higher than MOSFETs'. Which means the power density (at a given voltage drop) is greater by the same amount, which exacerbates the development of hot spots on the die that much more!
Of the few IGBTs I've seen with fully specified SOAs (I forget if they included DC, but several pulse widths anyway, e.g., 1us, 10us, 100us, 500us..), the limits drop very sharply with time. Which means, it's *very* sensitive to developing hot spots, and subsequent 2nd breakdown.
(Funny, I think vacuum tubes have similar limits too, though for very different reasons. Cathode current is limited due to wear -- something about space charge, electric field at the surface, interface chemistry, and who knows what other poorly-understood things. Plate voltage is limited statically due to arcing around the glass or between electrodes, but dynamically also, due to ion bombardment (reduces cathode life even further), sputtering, generation of x-rays and so on. There are only three types of vacuum tubes designed for high voltages: those with low temperature cathodes, made for pulsed operation (sweep tubes, radar modulators), where the low duty cycle gives acceptable life; those with low temperature cathodes, including ion traps (such as some CRTs) and low currents, to deal with wear; and transmitter types with more robust, high temperature cathodes, intended for quiescent operation at 30kV and beyond, but usually not for high current pulsed applications, or very high frequencies, which are usually served by the first class. There are also gas-filled e.g. thyratrons, but the higher gas pressure actually reduces cathode wear, allowing much greater current flow -- at lower voltage drop, which is key. But you also can't use it as a linear amplifier.)
Tim