The problem with most off the shelf first aid kits is that they are worthless with any severe injuries and this includes large cuts. I had a coffee pot break apart in my hand in a hotel room and after more than 30 minutes no one in the hotel could locate a first aid kit. I got some duct tape from the hotel maintenance person and used the tape to stop the bleeding and then drove to the nearest drug store to get bandages large enough to use to replace the duct tape.
Now I always take a kit I put together which includes large butterfly bandages and Quikclot packets that are good for stopping bleeding as well as pain killers and antibiotics. I also have a roll of duct tape handy.
Some of the better kits are made for mountaineering and offshore sailors and they include "flash" cards that walk you through the procedure to follow for any type of injury. Much better than a first aid book in an emergency.