The issue with the final tow-in to the gate is a well-known problem at LAX. At 12:30 am, you have a MEM flight pushing at 12:27 and an ATL flight pushing at 1:05. My guess would be that at 12:30, they're down to one or two ground crews to handle these last flights of the evening. Further supposition would lead me to think that what happened here was that you got the MEM crew handling this late arrival after the MEM flight pushed back. With pushback and engine start, plus repositioning the crew to another gate, 25 minutes doesn't seem that far out of line if another crew is handling that 753 heading for ATL.
The real problem here isn't Delta or levels of staffing; it's an airport that was conceived in 1960 and which is badly outdated for the amount of traffic it handles. LAX needs parallel concourses like Atlanta and that ship sailed 30 years ago when they opened the Bradley terminal and T1 which basically locked in the current inadequate terminal configuration, which consists of former satellite gate areas designed for the era of the Electra, DC-8 and 707. Like SFO and its prop-era runway configuration, California's major airports are almost all second or third rate compared to modern state of the art design. LAX could have been fixed years ago but it wasn't, which leads to the mess we have to live with today. For all the money recently spent on upgrading T5, it is still tantamount to putting lipstick on a pig. Too many flights, not enough ramp or gate space -- the picture is pretty obvious and it isn't pretty, What needs to happen for DL is that Alaska moves to the comparatively little-used T2 and 3, which would open up some space in T6 with a bus running to handle the AS codeshares. At this point, with DL sandwiched between AA and UA, it's about the only option left.