Since we never have any control over the size of the next toothy fish that's going to hit (may be a little guy, maybe a railroad tie), it's smart to plan for the big ones, as you point out.
One of the reasons that I came up with that frog-tube fly the other night is that I can retrieve the fly from the surface if the fish cuts the line. It would be great if we could do that with all flies, however the only way to do so is to fish tube-poppers all the time, and that's not realistic. But I digress... Heavy mono is what I've always used, simply for the reason you state: bycatch. Essentially, I tie the shock tippet to the leader with a loop-to-loop, which allows me to have flies pre-rigged and easy to change once the leader has been frayed. The larger the fly is, the heavier the leader material I use. Yes, little fish will often go after a large fly, however just as often you're going to hook into one of his larger relatives, and that's when the heavier leader comes into play. I wonder if coating the leader with Devcon would increase the durability of it? It sure would help the leader sink and straighten it out. BTW - I've used anything up to 50-lb. test as leader material.