The single-engine Bell Aircraft P-39 had a nose landing gear as well, in part because the engine was located behind the pilot, providing room for one.
I haven't been able to find a Douglas justification for the nose-wheel landing gear arrangement. My guess is that it made loading of torpedoes and 2,000-lb bombs a little easier because of better ground clearance and they could be lifted into place more or less level, instead of having to be tilted nose up to fit in a bomb bay or be aligned with cruise-flight air flow.
The Blackburn Firebrand torpedo bomber featured a two-position torpedo mount that provide both level load/ground clearance and low-drag alignment once in flight.
The nose landing gear didn't seem to provide any benefit otherwise (a Douglas evaluation did note that that a bad landing was less likely to result in the airplane bouncing over the barriers). On a single-engine airplane it significantly restricted the space available for a bomb bay if low-drag carriage of bombs was desired.
Nose landing gears could also be at risk of collapse following an inflight arrestment.
In any event, the next Douglas design, the BT2D, had a tail wheel. It was subsequently redesignated as the AD when the carrier-based bomber designation system was simplified to one mission, attack.
In part as a result of its preference for tail-wheeled landing gear, the Navy lagged the Air Force in adopting trainers with nose landing gears, trading off a somewhat higher accident rate for an earlier and more thorough indoctrination in the art of landing a taildragger.
For more on how the Navy transitioned its pilots to tail draggers after its changeover to trainers with tricycle landing gear, see http://thanlont.blogspot.com/2015/09/taildragger-transition.html