Consider that despite billions in investments, both DHL before they went away and FedEx Ground today are still not as good as UPS.
From the shipping side , with it's prime program they're so much better then other e-commerce competitors, that they won't gain much customer lockup by buying DHL(altought it might make them money), and they'll pay a big price.
On the other hand , if they'll control the customer, they'll have enough market power to force DHL or some other shipper to their terms. And with today's IT system two companies can have deep integrations if they want.
That would be a bit too vertical for my taste. I'm not sure massive hassle of trying to staff & run their own to-the-door shipping empire would beat the UPS service I get now.