Because they have no aircraft with approved powerback procedures in Delta's operating certificate.

Delta could do it with the NW DC-9's, if they still had any. The DC-9 powerback process was developed originally by Republic (or earlier by Eastern?), with the details worked out & approved by the manufacture & FAA & the airline and recognized in Republic's operating certificate. NW got those approvals when they merge with Republic.

The weight of the parked airplane flattens the tires, which require extra thrust to get rolling. Starting in reverse with enough thust to roll would tip the plane, so they go forward first, towards the terminal , then reverse.

For the most part, Northwest quit doing powerbacks for reasons of fuel economy. They were brought back during the mechanics strike in 2005 when they didn't have enough people otherwise qualified to drive the tugs (had been part of the striking mechanics' contract).

Delta could probably get approvals to do them with their MD-9x & 717 aircraft, if they wanted to. Delta has been rather sensitive to fuel economy issues, so that seems unlikely.

Generally, any high-wing aircraft would be able to do powerbacks (low-wing aircraft w/ engines under the wings kick up too much debris). The only aircraft I aware of that still do powerbacks are high-wing turboprops (Q400, ATR-72) and the C-17.