I work in a military fire station. We have those battle dressings on every rig, and train with them as well. I've been a Nationally Registered EMT for...over 20 years myself. I've used them, and they work.
And for those that haven't seen one...they are simply large gauze dressings with cloth ties on them:
There are some like products out there for sale. One is called The Emergency Bandage. Some have made improvements to the product.
I agree with the others...you can never be TOO PREPARED. Things happen when you least expect it. I have a first aid kit in the travel trailer, in the tow vehicle, and in the home. (and fire extinguishers too!)
Never hurts to take a first aid class either. Come up my way...I'm an instructor!