tl;dr
It’s not the freaking out that hurts them so much as the lack of freaking back in on the rebound
Bottoms occur when the last people panic sell. People tend to extrapolate trends poorly.
Who do you think shorts are buying from? Panic sellers.
But anyway, in equities, which is what most people invest in, the longs greatly outnumber the shorts. So short covering has a much smaller impact than a reduction in panic selling.
Shorts usually cover once the rebound starts, not when things are free-falling (their trailing stops get triggered, etc)
Mar'20, 2008, etc - these did not happen because guys were getting margined. These happened because because were panic selling huge amounts of length.