Having brushed parasites off a wild mola once (shame on me, I couldn't resist) I can say that the fins are far more soft than the body. They're still rigid but they aren't hard and armored feeling like the main body.
They're probably easier to chew and I'm sure the seals eat them (the sea gulls certainly aren't flying off with them). Perhaps the seals fling the molas to try to get scraps thrown off. Still seems a like an enormous energy expenditure in my mind though.
