Do you plan to nerf all the monsters as well? CR is established assuming the strong ones stay strong.
With that said, your suggestion seems to have merit.
However, the line, "The Monk (The Most Balanced Class in the Game)" makes "Balance" mean mediocre across the board.
Again, mediocre in comparison to what? The Fighter? The Wizard?
You're looking at this from the wrong perspective. You don't balance against other classes, you balance against the game world.
The classes need to be balanced against the game world. A wizard, who can effectively do anything is wildly overpowered and needs to be dramatically toned down.
But, let's do it your way... Fighter v. Monk.
What does the fighter bring to the table, really? Damage, buffing (due to his usually higher AC and pool of hitpoints the fighter negates the need to heal others) and a limited number of control abilities.
He might bring significant damage and he could have potential for absorbing blows, and he might trip like a madman.
What does the monk bring? A host of skills, from sneaking to diplomacy, and though he lacks the fighters hitpoint pool he brings the immunity to disease, poison and a natural resistance to magical effects to the table. A ray of enfeeblement that would make a fighter useless unless he possessed magical protections (which consume wealth or spellslots) is casually dismissed by the monk who was able to spend that wealth on other goods).
Is the monks ability to deal out damage and absorb direct physical punishment on par with the fighter? No. But the fighter doesn't possess the wide variety of often very very useful features the monk does.