Doesn't hold water for me. Do you have some specific idea about how this law only had this effect decades after it passed?
Obviously this also happened against the background of a broader trend towards deregulation that proceeded under Reagan, so it's not just that act.
Modern trucking is nothing like that, and often they are independent contractors in name only, driving someone else’s truck and being evaluated against strict performance criteria.
Edit: Also, Wal-mart's standards are incredibly high -- several years of clean driving experience. Most commercial truck drivers do not meet those standards. Despite the high standards, they still readily fill their positions. If they were having troubles, they'd lower their standards.
I'm sure it's like any job -- everything else can be great, but if you get stuck with a bad boss it can make you absolutely miserable and drive you out.
Of course, they had people fighting for those jobs, and from what I heard, about the only way to get one was to know somebody on the inside.
Up your pay, give them benefits, and the people will come. This isn't hard to figure out.