They may not cancel flights solely because they're not full enough, but why, if they're short a plane due to some problem, would they not choose the less-booked flights to cancel rather than the heavily-booked flights?

And, as mentioned above, why would any airline?

So the only way this is Southwest-specific is that they may have more planes out due to maintenance than some other airliens. So much so that it's the news about them getting fined multiple times for not doing enough maintenance before!