Ck,
It is said, that to eliminate all vibrations from a .22 short, the barrel would have to weight around 300 lbs.
To answer your question, muzzle brakes reduce recoil, they do not eliminate it. When a bullet leaves the barrel, there is a huge release of energy. This is initiated by the spinning bullet leaving the confines of the bore.
As the bullet spins free, it causes the weapon to twist in the opposite direction from the direction of bullet rotation. This movement creates a force refered to as "torque". As the bullet clears the muzzle, there is a massive release of gas pressure which drives the weapon backwards towards the shooter which is refered to as "rearward thrust". If you combine both torque and thrust, then you get a third movement defined by shooters as "muzzle climb".
The combination of these three actions are known as "bullet exit recoil". This isn't the only recoil we feel, but it is the only kind that muzzle brakes and porting can realistically address. If you were able to somehow harness this escaping energy and use it to oppose "bullet exit recoil" then in theory, you would be able to stop recoil (or most of it).
Years ago companies floated the idea that with screw on muzzle brake designs, you could install the brake to help get you through the "painful" chore of sighting in the big kickers and then remove the noisy objects while hunting without hurting your accuracy.
That sounds wonderful until you get a pre-schooler asking questions like "if the muzzle brake is that effective, how can removing it not affect your groups?". OOOOPS! didn't think of that...
I contend that if you had one of the thread on muzzle brakes in your hand and was able to time it just right to where you could expel enough energy to throw the brake behind you at the exact time you touched off the round, you would not notice the recoil near as much. Though you would probably need a bucket full of muzzle brakes to get you through a shooting session.
The pros: Able to get back on target more quickly for a quick follow up shot, Depending on the caliber, able to watch the results of the bullets impact on the target, and drives unwanted people out of your "space" while sighting in.
The cons: They are loud and obnoxious, there are more places for water, snow and debris to enter the bore and if they should come loose they can be a source of schrapnel.
Malm