from the "XTR is ECC but better" paper, an example of the reasoning you absolutely cannot find in ECC papers. note the reference to the MOV embedding (menezes-okamoto-vanstone) -- that's the 1993 paper that identified the issues with supersingular curve computation.
note that instead of relying upon the hardness of discrete log, it's "discrete log within the XTR supergroup", exactly equivalent to the claims made by ECC advocates. i personally don't trust it as much as discrete log but if i can get really small public keys and faster computation while actually understanding that i'm computing in GF(q6) and not GF(q) then i would totally take that offer up