Did the cost of shotgun shells increase significantly due to the requirements for steel shot?
You are missing the point: in many common calibers (including .30-06, 7.62x39, and .223), steel rifle rounds are ALREADY PROHIBITED!
A steel round in a rifle is a recipe for disaster.
A shotgun fires a mass of pellets down the barrel. Steel pellets simply bounce around the barrel.
A rifle has a MUCH different operation.
I will use a .308NATO caliber as an example.
The main part of the .308NATO barrel has an inside diameter of .3 inches. It also has groves that are .004 inches deep, and these grooves run the length of the barrel and provide a slight twist on the projectile. The bullet is .308 inches in diameter. So from the outside of one groove across the barrel to the outside of the opposite groove is .308 inches.
When the gun is fired, the firing pin strikes the primer and sets it off. This ignites the powder in the cartridge. The cartridge case is made of metal that is soft enough to expand slightly, to seal off the side and force all of the explosive power down the barrel. The bullet (the solid projectile) hits the chamber (cone shaped at the rear) and is forced into the barrel proper. Since the bullet is slightly larger than the barrel, the soft metal (lead, copper ect) is forced into the grooves. This makes the bullet follow the twist of the grooves to provides the spin which aids in stabilizing the bullet during flight. This is why rifles are more accurate than muskets. The rate of twist can vary, depending on the intended weight of the bullet.
If a steel bullet were used it would not conform to the grooves in the barrel, but would become a plug. The force of the explosion would then have to find another way out, typically back towards the shooter.