UPS does actually do something like this. If you buy a UPS label online without an account, you pay what's called "list price," which is the full advertised price for shipping. However, if you're a shipper with an account, UPS will discount your shipping below list price if you do a lot of business with them. I've seen up to a 20% discount for parcels shipped UPS Ground on a small company's account.

I don't have any data on this, but I suspect that some combination of the list price discount and some special contractual arrangements are what allow Amazon to offer services such as Prime for such a low price. List price for a 1 lb next day air shipment were on the order of $50.00 last time I shipped anything.