Gain twist became prevalent with the evolution of high velocity cannons. There is a limitation to the shear strength of the driving band when launched over the more energetic propellants at higher pressures. There is a secondary effect of reducing the pressure applied to the leading side of the rifling which increases barrel life.
The influence of the throat geometry will effect the pressure rise rate and peak pressures can be observed to change with the major diameter. Surprisingly as long as the cross sectional area of the bore is maintained the minor diameter does not have a pronounced effect (Notes for classical projectiles, I would not suggest that the minor bore is undersize for a typical cannon) The solid brass/copper projectiles are somewhere between a cup and core design, I do not have results.
From pressure testing it is possible to denote an increase in pressure related to twist rate but this is not seen until twist rates of 1 in 6 or below and is often masked in the barrel to barrel noise. I have no testing related to a 3 twist but conjecture if the effect becomes more pronounced but still minor.