So I'm assuming that the carrier could be just any ol' person who signs up? And they'd be responsible for the long-distance portion of the shipping? The issue I see is that: 1) I can't imagine that worthwhile compensation for individuals would compete with prices of major distribution 2) there's a serious risk of uncertainty with what happens with your package, and an inherent risk of inconsistency in service.
Shipments would be in some kind of secure container that could only be open once it reached its destination. There would also need to be some sort of verification on you and your vehicle. The idea is that your driving somewhere on vacation anyway, why not pickup something and get paid to drive even if the money isn't amazing. Imagine if you had to commute from LA to San Diego every week you could pick up a decent amount if you took something both ways every time you went. I agree there is a inherent risk of inconsistency with the service. But US Postal could spend a lot less shipping 3rd and 2nd class mail crowd sourced and sending first class in the traditional method.