Do you understand why your competitors work? They've spent decades building up brands like "When you abso-fricking-lutely have to have it there by the day after tomorrow, or it's your job." There are movies about their core value proposition and brand messaging. Now after you understand how they work, do you understand which of their customers don't need to pay for that? Can you identify a group of folks currently sh…
The problem space being addressed is more complex than what it looks like. Customer perception of reliability is everything. Shipping companies have made their offerings as reliable as banks. There's numerous safeguards in place to protect the customer in case of an accident and you have professionals handling your valuable items.
Perhaps an ebay-like system of feedback will help eliminate some of the wariness that accompanies a total stranger delivering your package, but even then the event of loss, theft, and damage will be much higher than it is with the existing shipping companies. That alone would make it difficult to get this idea off the ground.