It isn't that hard to exhaust the contents of any normal FAK and who says you will be dealing with only one casualty in an incident?

On one operation with one seriously banged up victim, I was now improvising splints, casting questing eyes at a small pine tree along the trail, and I had removed my pants to use them for splint padding. I had another pair in my pack and treatment and stabilization was a higher priority. This one victimnearly exhausted my fairly extensive FAK.

You might even have to use a non-sterile material to staunch blood flow in an extreme case. Not recommended,, of course but if you can deliver a patient to the ER still containing appropriate liquids, they have the resources to compensate for infection.