If you stop a tuna, you stop it breathing. That's why most of the old timers used 400 lb handlines. They do their first run, then had the screws put to them. Takes very large fish out of the fight.
Like Niko said, the longer the fight, the more chance of something (hook wearing a bigger hole, knot failing, etc etc) going wrong. Best to put the heat on ASAP and keep it there. Better for the fish, too, if you're going C&R at all.
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