When I wrote 'What would a startup do that they couldn't?' I wasn't asking 'What services would a startup provide for end-customers that aren't provided by existing couriers?' I was asking 'How would a startup make a profit in this hard-to-enter market when Amazon, with all its advantages, has apparently decided it can't?'
Do you think Amazon couldn't provide realtime tracking or SMS notification? Those things are frills. They'd be nice. Maybe a few end-customers would pay slightly more for them. But they don't help you with the real problem, which is setting up a hub-and-spoke delivery network that's fine-grained enough to get a package from a central warehouse to any individual house in the country within three days for less than five bucks.
You, the person waiting for your package at home, are not the customer. The customer is Amazon. What the customer wants is delivery that's sufficiently reliable that it doesn't cost them business, and sufficiently cheap that it doesn't interfere with their efforts to undersell traditional retailers. Can you make them a viable offer on those grounds? If not, SMS notifications aren't going to change their mind.