In many ways, I think that I can land a fish as fast or faster with a fly rod. Having said that, I my impression is based on watching others with convetional tackle fight fish. My skills with the hard stuff is limmited.
I also think that a 40# weakest link not safe with fly gear, and I don't think that there is a fly rod that is stout enough to take advantage. Only a couple of reels. Watch your fingers..
Tuna and Marlin on a fly rod is "light tackle". Tarpon and Sail Fish can be brought in relatively quickly. I saw Stu Apt bring in a 90# Tarpon in about seven minutes. I watched carefully, and I didn't notice any cuts or edits. That's fighting a fish!
One cast can change your day...maybe your life.