I read somewhere that the maximum force required to free a bullet from a crimp is approximately 100 lbs. Going back about 40 years to my college Engineering Statics course work indicates that this force is dependent to a large extent on the diameter, so guessing here that 100 lbs. was probably for a 50 BMG. With 1/2 the diameter and 1/2 the circumference a 50 caliber rifle bullet will peak out with a pull force of 50 lbs.
Now, the required pressure to exert that level of force will be equal to the Force divided by the Area. With a circle the Area is (1/2 Dia) squared time PI, or 1/4D^2 x 3.14159. For that 0.25 diameter rifle bullet that area will work out to 0.049 inch^2. So, 50/.049 = 1018.6 psi. What this means is that the pressure induced by a firm rifle crimp will only require something around 1000 psi to get the bullet moving.
While that isn't a lot of pressure a recent experience when I forgot to crimp some 223 ammunition loaded with CFE223 reveals that some powders do need a bit of help with a rapid pressure rise in order to get a good clean burn going. So, while a crimp may not actually contribute to the peak pressure produced during the complete firing cycle I do believe that a crimp can be an essential element in producing a clean shooting and accurate round of ammunition. Currently the two powders that I consider a crimp to be absolutely essential with are the CFE223 as mentioned and H110, a Handgun Magnum Powder.