dV/dt is a failure mechanism in diodes and in MOSFETs.
Diodes, I'm not clear why. Also it's specific to schottky, I think?
In MOSFETs, the parasitic BJT can be turned on, potentially drawing extra current during a rising edge (so, switching loss with a "tail" of recombination current), but also potentially biasing it into the pulse avalanche regime where it turns on suddenly and extremely quickly, causing device destruction.
The BJT has low hFE and is normally shorted B-E by the source contact (i.e., source and substrate are shorted together, it's right there in the symbol!). So it takes a lot of dV/dt to couple enough current through the junction capacitance, into the bulk resistance between those (B and E) regions, to cause this effect. Typically some thousands V/us, 10k being pretty common.
SiC is fast enough that I suppose it's an actual risk. I don't think I've ever made Si go fast enough that it's nearly a risk.
As for faults, keep in mind SiC dies are impressively tiny -- there is very little bulk to dissipate power into, so the allowable short-circuit time may be quite short. Si MOSFETs might withstand for 10s, even 100s of us; IGBTs typically 5-20us; SiC maybe somewhere inbetween, maybe less. (Power GaN are even more severe still, with the full SOA barely being available for 1-2us. Very power-dense indeed, this is no surprise.)
Note that desat detection works just fine on MOSFETs, you just may need to set the threshold voltage higher (above Rds(on,max) * Id(max)). Been there done it.
Tim