As dave54 pointed out, at some point you have to make trade-offs. I have a pretty cautious (downright paranoid?) approach, so I carry a fairly big first aid kit. I started with one of those pre-assembled "Adventure Medical" kits and then removed some items and added others. Lately I've been thinking about dropping more items to save weight and bulk. But I'm surprised no one has really brought up my biggest concern.
As others have mentioned, you can use other gear as first aid gear in a pinch. A bandana as a sling. A bite valve for wound irrigation. Duct tape as a butterfly bandage. (I'd prefer not to get too carried away with this approach though. It might be difficult to think creatively and clearly enough about gear improvisation when you're hurt and possibly suffering from shock, or panicky with concern for another's well being.) And of course, you can simply do without certain items - not having a knuckle bandage for that minor cut is probably not a serious issue, for example.
But one thing that you cannot improvise is a LARGE, STERILE dressing. You can improvise a non-sterile dressing from clothing, but these days much of the clothing worn or carried by most hikers is made from extremely non-absorbent synthetic fabric, making it totally unsuited for the purpose.
Yes, you're much more likely to have an incident involving minor cuts and lacerations than a major wound with serious bleeding. And it's nice to have all those different sized bandages and tweezers and whatnot. But what do you really NEED to have with you if something serious does happen? Large sterile dressings (sanitary napkins are a cheap form of this), roller gauze and tape are far more important, in my humble opinion. Just something to think about.
“I don’t deny that there can be an element of escapism in mountaineering, but this should never overshadow its real essence, which is not escape but victory over your own human frailty.”
- Walter Bonatti