This is largely in part to the same reason New York's subways are stuck in the 20th century: Unions. While they serve a vital function to prevent labor abuse, nowadays they are abused to prevent innovation.
There is currently no technology that would allow UPS to fully automate, nor would even gain enough efficiencies that would repay the investments needed. The amusing thing to me is - now is probably the right time to fully automate sorting, the technology is much more mature and will likely have a longer lifetime before replacement, than the technology FedEx just installed.
NYMTA, could fully automate - but as a cost greater than building new subways from scratch - the largest issue NYMTA has is a lack of local control, a lack of funding (from Albany), and the tact that if the subways - any of them - shut down for any amount of time, the city devolves to gridlock.
Complicating factors for MTA are, outright corruption, an indifferent management, regulation that makes construction difficult, and a top down safety culture - that prioritizes eliminating the /appearance/ of risk, over reducing realistic risk.