I have a question about the emphasis a lot of you are putting on heavy lines/shock tippets and playing the fish quickly.
It has always seemed better to me to let a fish tire himself somewhat before the unhooking, so that I can lip him calmly and remove the hook without the fish flailing about, tangling itself in the leader, bonking itself against rocks or sand or boat or whatever I'm fishing from, and requiring me to grab a firm hold on its body in order to free it.
Even barbless flies (which, of course, is the only way I fish) can get gnarly in a striper's mouth, as you will often have multiple points of entry. [i.e. through the upper lip, back in the outside of the cheek, lodged in the mandible]. I think it's a lot less damaging to be able to control the fish during this process than to have a relatively unplayed fish thrashing itself free while you just keep a firm grip on the shank of the fly.