I'm going to play devil's advocate for a bit, as there don't appear to be any ichthyologists or fisheries scientists posting. Both however are sub-disciplines of my field. Feel free to correct any mistakes I might make.
1. Jacques Costeau was not a true marine biologist. Very little use of the scientific method, and non-rigorous protocol designs. He's what we commonly term "national geographic scientists", or "sensationalist scientists". A more appropriate (and well-merited) designation for folks like him are underwater explorers. They're role is more to introduce the public to the natural world, rather than to perform research. They're indispensable as educators. They sell pretty books too.
2. Rationale for gut content analysis. Older, larger animals often have different dietary habits. And we really do know little about the behaviours and trophic dynamics of pelagic animals like makos. Often the information gleaned from books has been taken from very small data sets. Many times they're inaccurate as a result of this.
Another reason. Makos primarily are apex predators, feeding on billfishes, scombrids, and carangids. As those stocks are all commercially fished, it is useful to know if the diet of their natural predators is showing signs of shifting. If that can be documented, you have additional evidence that fisheries are being overexploited. "Lack of evidence" is the parrot-cry of fishing lobbies, and one of the top reasons regulatory action is slow to take form.
3. Rationale for aging specimen. Above-average sized wild organisms are always of interest to science. We'd like to know why they're so big. Is it age, diet, sex, environmentally, or behaviorally motivated? What is the animal's reproductive status? Are there biomagnified compounds in the tissues reducing fertility?
Growth rates and fecundity are among the Top 5 measurements of importance to fisheries scientists. They're necessary in predicting and modeling stocks. Shark fisheries rank as among the most poorly known. This lack of knowledge severely hampens our ability to pass regulations.
4. Public aquariums are not a better venue for a captured animal. It's far more useful to get data from a wild specimen. The only real advantages to aquarium transplantation are public education, and to ease the minds of the animal cruelty demographic.
5. It's well documented that experiential education is a very powerful and lasting resource management tool. I'd take all the kids I could to tournaments like this. It all hinges on how the experience is managed by the chaperones. With well-versed educators leading the group, you're going to do a lot of future good. The net gains can easily outweigh the losses. As an experiential marine educator for children and college students, this is a no-brainer.
And yes, dissecting large sharks killed by fishing efforts really DOES turn off kids. I've got 23 teens that'll attest to it.
*** one more thing, for the critics of the "shark steaks". Remember that much of the tournament would have caught smaller specimens perfectly acceptable for human consumption. And grilled mako does happen to be one of the tastiest of sharks. I do agree that caution might be warranted with eating the flesh of giant specimens... however biomagnification is most definitely NOT universal in the marine realm for large apex predators.