One way around this is to have your sender mail it with signature required. That's a giant PITA for you, but that way they can't just leave it. There are those who love to steal packages left by front doors, etc. and for regular priority mail, that's what they do.

I have a relative who runs a coffee business in Hawaii and ships the good stuff all over the place. Virtually all of it is USPS priority mail and in talking with him, he has to reship occasionally for exactly the same reason you're describing, but ultimately it's cheaper than shipping UPS or FedEx even including the ones he has to reship. If a customer demands it, he will ship UPS and pass the extra expense on to them.