I fully understand what you are saying, AND the principle involved - but the usual practice is to take up the slack to the point that the strap is off the ground, then start the pull at a firm and steady pace. In this case, the guy in the tow vehicle applied force and MOTION at too great a speed - and the strap didn't heve the strength at that rate of application to overcome the resting mass of the load - the strength of the strap was likely adequate, but not at that rate of applied load.
Here's an experiment in physics for those wanting to see this in action:
Take a length of common string, and tie it around a 10 lb. or so rock - and then tie another length of the SAME type string around that same rock to dangle below the rock as you suspend that rock from a secure achcor point by the upper length of string.
NOW, gently and steadily pull down on the dangling lower string - and the TOP string will eventually break as you increase downward pull - THAT demonstration shows what you WANT to happen in the truck towing bit up above. The breaking of the TOP string represents the pull on the LOWER string (tow strap)
overcoming the mass of the
LOAD (stuck truck), and breaking it free.
NOW, restore the top string, and again repeat the pull on the lower dangling string - but THIS time just give a quick and sudden YANK on it - and the BOTTOM string (tow strap!) will
SNAP because it's strength cannot overcome the resting mass of the load (stuck truck) when too rapid motion is applied!
All the same string and load - just a different application of force.
Plain and pure basic physics based upon Newton's law of motion - and it works the same EVERY TIME! :-laf