Well, this thread turned out to be super interesting!
Yes, I'm young and don't need painkillers much. If I had frequent pain, where knowing the extent of it wasn't important to me, I'd bring painkillers.
The diarrhea threat is a good point to make, especially on a longer trip. I've considered carrying a small vial of salt on longer trips in case someone loses the ability to hold down solid food. I've also decided to take a decent amount of liquid food on longer trips - sometimes I mix Nido and Swiss Miss cold as chocolate milk, so I just bring a fair amount of that. It's good to have liquid calories as an option. I used to always just pre-package any not-so-salty food with extra salt, but I'm thinking of changing my tune on this, at least on trips longer than a weekend.
As for life-threatening bleeding, my thoughts would be direct pressure and if you need a bandage, improvise from clothing. Of course, if everyone's a lightweight backpacker you probably don't have much spare clothing. I do carry a bandana, which could be a tourniquet, allowing time to apply an improvised pressure bandage if the wound is too bad to be stopped by direct pressure. You can't keep it on for days, but for a few hours it's fine. For those who haven't taken a recent WFR or WFA, the wilderness medical schools have changed their opinion from a few years back on tourniquets based on knowledge from the military. I would have no hesitation using one in a situation of bad bleeding.
The closest I've come to serious injury on the trail was a rock that could've broken one or both of my legs. In the worst case it could have killed me instantly. I dodged it barely and it hit my arm, leaving me with just a small bruise. That's one of the incidents that's made me wonder about first aid. But again, improvised tourniquets could save a life here, and in that case we had cell reception (on Powell Plateau in the Grand Canyon, at over 7000 feet). We also were a 4-person backpacking group, all wilderness first responders. Breaking a leg in a truly remote location is such a rare occurrence that I wouldn't plan my first aid kit around it, but it is a good thought exercise.
Jennifer: all I can say is OUCH!