Well - as had already been pointed out - even just cutting off the dorsal fin of shark - will reduce it's ability to hunt and swim. It's basically an injured or crippled predator. And in the wild, injured or crippled predators don't last long.
Also breeding sharks in captivity for the fins isn't a practical Idea.
Here's why. Generally those that kill sharks for their fins - aren't insterested in coastal species of sharks or small species sharks. While many of these coastal species such as Nurse sharks, Bonnethead sharks, & Smoothhounds, or small species such as Horn sharks, Bamboo sharks, or catsharks have been successful kept and even breed in captivity.
Most the species favored by illegal shark finners - tend to be species that are oceanic, and therefore are species that don't tend to do well in captivity, and have never been known to breed in captivity. Species such Blue Sharks, Makos, Oceanic Whitetips, Hammerheads, & Blacktips (not the Blacktip reef).
