A muzzle brake on a 243 pushing a 55 grain bullet at 4,000 FPS with 40 to 45 grains powder has significantly more recoil than a 22 long rifle. The powder has mass and is an ejectorate the same as the bullet and needs to be included in recoil calculations. Best example I can give is I have 2 identical Tikka 595 Master Sporter's with Krieger Barrels. They look like this one without the brake.
http://www.tikkashooters.com/public_...tikks-595-6xc/
One is chambered in 6mm BR and the other is 240 NMC. Same scopes and mounts with a weight within 1/2 oz of each other. For the same velocity with the same bullet the 240 NMC uses about 10 grains more of the same powder. Recoil of the 240 NMC is noticeably more than the identical 6mm BR.
For prairie dogs I use brakes on .223, 6mm BR, 6mm XC, 243 and 6.5 x 284. The .223 is used the most and the most used of my 223's is an AR with 28" heavy weight Krieger barrel with the gas port extend out two inches. Using 40 grain Nosler Ballistic tips or Hornady V-Max I am getting 3,800 FPS. I have lead in the stock and total weight is 14 1/2". The brake does prevent the muzzle jump enough that self spotting impacts is easy, however, recoil is still significantly more than than my 11 pound 22 lr target rifle. Same weight bullets but about 25 grains more powder with three times the velocity. Very curious how your recoil calculator claims about the same as a 22LR for an even heavier bullet with more powder?????????
Apples to orange for the style and type of rifle but my 6mm XC using 55 grain bullet recoils more than the AR but it should since it using 12 grains more powder, 15 grain bullet and an additional 200 or 250 FPS.
Your premise that recoil in and of itself decreases accuracy in flat wrong. Recoil does introduce additional variables that if not dealt with effectively will change point of impact or open up groups. No surprise there. Same for an improperly fitting stock.
You seem very impressed with rail guns. Have you ever shot one? Seen one in person?
Rail guns actually disprove your case since they remove the recoil induced human influences. Rail guns don't care if is a 22 PPC or a 50 Cal BMG. The most accurate of the rail guns are the Militaries artillery pieces. If recoil was the only issue they would be the least accurate.
Rail guns are not a given to win the classes. Check out the light and heavy gun aggs. verse the rails guns.
http://bulletin.accurateshooter.com/tag/light-varmint/
http://bulletin.accurateshooter.com/tag/rail-gun/