This came home to me in the summer when involved in a rescue. When asked to contribute first aid kit only 5 out of the group of 15 had something beyond the 'compspeed/brufen' kit. All who contributed had completed a Wilderness First Aid course.
One of the chaps who taught the course where I got my outdoor-oriented first aid certificate was asked what he carried as a personal kit. He replied he didn't bother (perceps excepting a roll of gaffer tape) as you could improvise most stuff from what you had. Obviously not stuff like pain-killers, but there's an important distinction between comfort stuff and survival stuff.
First aid is mainly about procedures, not stuff.
One occasion I ended up involved in a rescue was after a cornice collapse had caught a climbing party at Craeg Smeggy. Various problems ranging from shaken and stirred to suspected broken back. I quickly dug out my reasonably well filled FAK and... found absolutely nothing I could do with it. The jobs were immobilisation and protection of the ones with breaks and suspected breaks, and keeping them warm and spirits up. So fleeces and snow-shovel were far more use than triangular bandages etc.
I carry a FAK, so I clearly think they're worth having along, but anyone getting the idea it'll save lives is probably wrong. What it might well usefully do is reduce discomfort to levels that mean a day isn't ruined by a minor mishap. In other words, compeed and ibuprofen are a pretty good thing.
Pete.