The straight grips on early trap guns are likely a carryover from the Pigeon guns. My Fox single barrel trap gun of 1935 vintage has a straight grip with a Monte Carlo. Straight grips were pretty much the norm on Remington Model 1894 Trap and/or Pigeon Guns. Throughout the period of manufacture of the Models 10 and 29 (and Model 11s during that time) the trap guns are always shown in the catalogues with straight grips, but would be made to order with a half or full pistol grip at 6 to 8 weeks lead time. Trap guns with capped full pistol grips are first shown in the Remington catalogues when the Model 31 arrived.
Jack O'Connor wrote that a straight grip slightly cramped your wrist and had a tendancy to make you shoot high!?!