Just to share 2 things on this topic.
The way I learned: I mash the barbs down on my flies. I do so because where a friend and I started fly fishing (Anchor River), we heard some of the locals/regulars there would give you the business if they saw barbs on your flies upon landing Steelhead. In a catch&release fishery, it made perfect sense anyways, so we didn't mind. In the years since, I haven't noticed much difference in fish landed - that is, when I fished spin gear in Florida with barbed hooks, I occasionally had fish spit a hook and I still do - with no notable difference in the frequency. It's not hard to keep the line tight and minimize the opportunity for hooked fish to spit. Those times when I get caught with slack line, it hasn't been a problem either. Just luck maybe, I don't know, but thought it interesting.
A different perspective of the resource: A few years ago, Dennis McAfee told me about a weekend trip fishing the Kenai. There was more to the story, but at one point he described the trout he saw as a bit "soremouthed". Now, I didn't ask him what he meant, the point of the story was something else, but I assumed he was referring to the small lip scars I see sometimes on larger Kenai Rainbows. It gave me a new perspective on the resource. These fish are large and fierce because they live long (with great nutrition on a river ideally suited to optimal conditions), but may be hooked repeatedly over the years.
I like mashing the barbs down - doing something for the resource. It's a personal thing. It has a way of sharpening my focus while fighting fish. When fish get off, I figure they won one round. I've heard guys call it "early release" - and an early release is probably healthier for Rainbows, eh? When landed, I have come to favor what veterans call "wet release" - release without removing the fish from water. A delightful fringe benefit of that approach has been the "wet" photos that I've taken the past few years look even better over the years. Thinking about all those healthy Rainbows and Steelhead in the years to come makes it easy and kind of rewarding.