You can get sabots that shoot 22 bullets in 308 cases, reaching 4000 fps in a 30-06. But that won't happen with a 22-06 unless you got a 30" barrel or something. The sabot still retains the .308" diameter base, which gives the sabot base a 0.0745 square inch area for the powder to push against, at 50,000 psi that relates to 3,725 pounds of force of the bullet.
A .223 projectile only has 0.0391 square inches of area, translating to 1,952 pounds of force with a 50,000 psi chamber pressure. That's only 52% of the force a .308 bullet receives.
I've seen 50-308 sabots that allow you to shoot 308 bullets in a .510 caliber rifle. The seller advertised 5,280 fps using a 168 grain bullet in a 50 BMG. The .510 sabot has a surface area 2.75 times that of the .308, so you can see how easy it is to get a massive amount of force on the projectile.
I realize that the chamber pressure is not at 50,000 psi through the entire burning process, and that a faster projectile get acted on for a shorter period of time than the slower one. The greater surface area is one of the reasons I chose the .358 Winchester as my new deer rifle, it can push a 180 grain pill at the same MV as a 30-06 with less recoil and a shorter barrel.