Supposedly physicians are terrible at triage, for the same reason. It just takes a different mindset, doing the most good for the most people.

Just to hammer a point made earlier, NEVER do more than you are trained to do, regardless of good samaritan laws, you can easily do more harm than good. The only time you should ever consider removing someone from an automobile after an accident is if you believe they are more likely to sustain a life threatening injury by remaining in the vehicle - i.e. the vehicle is on fire - otherwise do what you can to support life with them in place.

First Aid Kit should contain only products that you are confident in using. If you don't know what it is and how to use it, it shouldn't be in there. Stick with the absolute basics of ABCs, as mentioned earlier.

Airway - held-tilt chin-lift or jaw thrust maneuver - no equipment for layperson is needed - you will NOT being doing a cricoidotomy! - although, I often wonder about suction... very useful, but suction devices are bulky.
Breathing - pocket valve mask, anyone trained in CPR should carry one of these or equivalent
Circulation - bandages in varying size (2x2s, 4x4s, abdominal pads), tape, gauze, trauma shears, cohesive bandages (ACE wrap), tin foil (for occlusive dressings), tourniquet -> only if bleeding cannot be controlled with direct pressure, elevation and use of pressure points!

EDIT: forgot to mention PPE!! I carry 2 pairs of nitrile gloves, a couple face masks (droplet precaution only), and safety glasses.

Never give meds unless they have a prescription for it, and are carrying it, just too risky.

That being said, I do carry a bottle of Benadryl, tylenol, chewable aspirin, and a tube of glutose for low blood sugars. Some people also carry activated charcoal for overdoses, but it's messy, tastes disgusting and people often vomit it back up regardless.