I have not read this post I a while. The decision to leave out some food to be replaced by fishing depends on your willingness to fish, your ability, where you are going,and your feeling about taking a chance of going without.
I find that backpacking and fishing go well together. I am not able to walk hard from daylight to dusk. Even with 8 hours of walking, in the summer, I still have time to fish in the morning and evening, when the fishing is actually better than during the day. I rarely fish for more than 1-2 hours. I only fly fish. The last few years I have been paying more attention to what other backpackers say about where the good fishing is located. I have been quite successful the last two years, both in the Sierra and the Wind Rivers (where it is really hard NOT to catch fish).
Remote back country lakes do not get much fishing pressure. The fish are pretty dumb and hungry. I am not a good fisherman (you would laugh if you saw me cast a fly), but I catch plenty of fish. As for matching hatch, never have done that. Those hungry high alpine lake fish will strike at anything, as long as they are feeding. And that is the key. Fish when they feed. Most often, cleaning the fish takes longer than catching them. The benefit of one 13" fish vs six 8-inch fish is the saved time because cleaning the one big fish does not take much more than cleaning one small fish.
By the way, the small fish are often brookies, and in most places there are higher limits on brookies - usually 10 or more.
I find it hard to find protein sources in dried food I use for backpacking. Easy to get carbs, easy to get fats, but much harder with protein. My backpack food is usually 15-18% protein as calorie percent. Fishing is a great way to boost that up.
As for extra fuel to cook, not necessarily so. I simply drop the cleaned fish in the pot as I cook the pasta, or rice, and then pull it out, take out the bones, and put it back in the one-pot meal. When I am where I can have a fire, then I fry the fish.
My fishing gear weighs 11 oz total. I go very minimalist. No net, use a spare shoelace for a stringer, one film canister of flies, one extra leader, no extra line, a split foam pipe insulation for a rod carrying case. I only take the amount of line that I can cast, and since I am lousy at casting, I do not have to take much! My light small reel is less than half filled. I also take a 1 oz paring knife. These are the cheap ones you buy for $2. They are really sharp for a while, but do not hold an edge. At $2, I just get a new one for each trip.
For me, the hiking is #1, photography #2 and fishing #3 priority. Even at that if I take my fishing gear, I drop my food to 1 pound per day vs 1.3 to 1.5 pounds per day without fishing.