Messenger warfare: I put same-day delivery to the test

The issue I see with same-day delivery is that for it to be possible for a startup to beat FedEx, UPS et. al on price, there has to be some aspect of delivery that the existing companies are doing wrong (or inefficiently), or there has to be some key innovation.

Take Uber, for instance. Uber succeeded because they were able to 'fix' the problem of taxi company monopolies- a problem with the existing market. Alternately, look at Google, which introduced PageRank, a massive improvement over existing search algorithms.

Existing delivery companies seem to be fairly sophisticated, and to be focusing only on the core problems of delivery. Unless I'm missing some crucial aspect of delivery, I don't see anything that FedEx or UPS could do differently [1] to cut costs & improve speed without massively increasing cost.

[1] The obvious exception is drone delivery, but I think that's a far too difficult problem to be solved by existing technology. I would love to be proven wrong though.