If you want to use a sawback knife, use it! I own several sawback knives, all customs that actually do cut. Not all sawtooth knives are cr@p. If you don't want to go into the woods looking like a Christmas tree with all of your gadgets weighing you down, and hanging off your body, go with the sawback knife. The saws on these knives are not for cutting down trees as many people seem to think, but for working bone, wood tools, making traps, and scoring branches to be snapped. Sawback knives are no replacement for a good folding saw, but they definitely have a place.
If you are putting together a lightweight survival kit, choose items that can have more than one function. But if you're giving yourself a 5 pound limit, more like a bug out bag, have fun with it. There's tons of great advice on this forum.
Surviving in the wilderness is not a planned activity. If you read true stories, it's usually people who got lost, a plane crash, injury, or other breakdown of some sort. I don't think anyone who was lost had a saw, an axe, food, water, backpack, shelter, compass, etc. All they had on them was whatever was on their body. There was a downed pilot in the Alaskan wilderness who's plane sank in a lake. All he had on him was a lighter and a Leatherman tool. With his knowledge and what he had in his pockets, he was able to survive over a week in the bush before being rescued.
If I got myself into an accident, and I couldn't get to my bug out bag, I'd only have the knife on my belt, when you boil it down, that's it. What one thing do you want on your belt if something bad goes down?