Back in the 70s when I was into mountaineering and rock climbing, I did a first aid course which was led by an ex military medic.
He started off by getting everyone to empty their various proprietary first aid kits out. He then dismantled the whole ethos of these first aid kits.
Most small first aid kits contained a range of band aids, antiseptic cream, aspirin, small bandages etc.
As he rightly pointed out, if your problem can be treated by aspirin, then live with it.
If it can be treated by a band aid, then live with it.
However, if you come by a real life threatening emergency, then the average first aid kit is about as useful as a chocolate tea pot!
His serious advice back then was to dump the band aids and use a 100 yd roll of sellotape, and a bunch of triangular bandages and gauze. A 1 metre roll of sticky plaster will disappear in an instant at the first real accident, and sellotape is obviously sterile anyway. Also forget trying to do properly taught Red Cross style bandaging, you won't have time for that, just lash everything together with as much sellotape as needed.
I took it to heart and dumped the superfluous junk, and added the sellotape roll and more triangular bandages and field dressings.
A short time later when half way up a rock face in the UK Lake District, I was alerted by someone running along the cliff face yelling at the top of his voice, "First aiders, any first aiders...... any first aiders..... please help we need help now."
I quickly descended, grabbed my stuff and ran after him. Apparently his friend had been half way up the rock face and had fallen, ending up tumbling another 100 foot down the sloping base of the cliff. He was badly gashed and looked a mess and most likely concussed.
That was the first serious call on my meagre skills and I can say easily that a normal first aid kit would have been utterly useless. Thankfully, the Mountain Rescue team had been called and we were not too far from road access.
The value of that roll of sellotape was proven beyond doubt that day.
Since that time, whenever I cut myself, I just wrap sellotape around it, much to the amusement of my wife.