What I share below is not a point in favor or against a driver paying from his or her own pocket the cost of being towed to a delivery if a breakdown under load occurs. It is just something to keep in mind as you think the question through.
As expediters, we tend to see loads one at a time, which is understandable since we haul loads one at a time. Diane and I did two loads last week. Some weeks we do more but a five-load week would be rare. Solo drivers do more, I presume, maybe as many as 200 a year?
Compare that to a shipper's view of loads. They may send an expedite load or two out the door every now and then, or they may send dozens a week. Additionally, they will typically send many more LTL and TL loads and individual packages. Where we expediters see loads individually, shippers see them by the dozens and hundreds.
Being leased to a single carrier, most expediters see things one carrier at a time too. But the fact is that very few shippers have exclusive relationships for shipping expedited freight. When they have hot freight to ship, they don't call one company to find a truck, they call several. That is the very reason why FedEx changed its dispatch system a few years ago to one that sends the same offer to multiple trucks at the same time; to produce a faster answer for shippers who call lest the shipper call someone else while the answer is waited for.
When we show up at a customers shipping or receiving dock and look the people in the eye, it is an important part of our day. But for the people on the dock and in the shipping and receiving offices, we are but one truck among many, from one of several carriers they see in a day.
We can do things to distinguish ourselves and our carrier at the loading docks we visit, and some of those things may even stick in the customers' minds. Far more influential are the failed loads and the vows customers take like, "I'll never use that carrier again." But for a customer who ships lots of freight, it would likely take more than one late delivery to prompt such a vow. And even if such a vow was taken, if the carrier in question is the only one with a truck available the next time hot freight needs to be shipped, the vow may be forgotten or suspended.
Also note that the turnover rate seems to be high among shipping and receiving departments. Diane and I have visited the same docks many times but we do not often see the same people. The person whose sox you knocked off with your impressive and expensive display of dedication to completing a load may not be on shift the next time you are in the area, may have been promoted or demoted to a different job, or may not be at that company at all.