Bullet energy, (and thus velocity squared), is proportional to the area of the bullet base times the area under the curve of pressure versus distance down the rifle barrel. The rate at which powder burns is an increasing function of temperature and an increasing function of pressure: Higher pressure = faster burn, Higher temp = faster burn. The velocity limiting factor with all modern powders is that the pressure peaks when the bullet is a short way down the barrel, and then it falls off rather quickly as the bullet moves farther down the barrel. To increase velocity, then, you have to figure out how to lengthen the peak of the pressure versus distance curve WITHOUT increasing the height of the curve (and thus blowing up your rifle), and/or figure out how to make the pressure v. distance curve fall off more slowly.
The "magnum" approach to higher velocities is to increase case capacity and stuff in more of a powder which burns more slowly. HIgher case capacity and slower burning powder keep pressure from building too quickly, and also provides a bigger reservoir of high pressure gas which is replenished with burning powder over a slightly longer period of time. It works, but there are serious downsides: 1) All that hot gas rushing out of the chamber erodes the barrel throat more quickly; 2) The extra powder increases recoil and muzzle blast tremendously (To calculate recoil, the empirical rule is that the momentum of the recoiling rifle will equal the bullet mass x bullet velocity + the mass of the powder x bullet velocity x 1.5. So... increasing powder by 10 grains increases recoil momentum the same amount as increasing bullet weight by 15 grains.); 3) To realize much increase in velocity, you need a magnum length action and a long barrel, which makes for a longer, heavier rifle with a whippy barrel.; 4) The long whippy barrel combined with a much greater volume of gas rushing past the bullet as it exits the barrel has a negative effect on accuracy.; 5) The law of diminishing returns kicks in very fiercely: A 10% increase in bullet velocity can require a 100% or greater increase in recoil, along with the longer, heavier rifle etc. I don't have any insight into the efficiency with which the chemical energy stored in the powder is converted to bullet energy as a function of burn rate, but I suspect that slower burning powders burn quite a bit less efficiently - which, if true, contributes greatly to the diminishing returns with this approach. At a minimum, overall efficiency is reduced because more of the powder energy necessarily goes into the kinetic energy of the powder gasses.
Progressive twist is interesting because it lengthens out the pressure versus distance curve like this: Because the rifling near the breech has a slower twist, it doesn't offer as much resistance to the bullet, so that at a given pressure, the bullet accelerates more quickly near the breech, and the effective length of the chamber in which the powder burns gets bigger more quickly. The faster increase in burn chamber volume reduces the rate at which pressure and temperature build, therefore allowing the powder to burn more slowly, and thus increasing the length of the pressure v. distance curve without increasing its peak. So.... you can put in more powder without exceeding peak pressure, that powder burns more slowly than it would in a rifle with fixed twist, the pressure v. distance curve has more area under it, and bullet velocity increases.
Progressive twist would seem to be particularly attractive when you don't have much control over powder burn rates - such as with black powder, or in the early days of smokeless powders when the 6.5 mm Carcano was developed.
