No, I don't.
Monks are a mobile DPR oriented character. BM Fighters are more versatile and survivable, but you apparently think they should not only be vastly tougher than Monks (higher AC and HP) but also do more damage and benefit more from magic items, and in any game with Feats, the BM Fighter already likely does significantly more damage.
Really hoping you blow my mind with some kind of mechanical insight here, don't just double down on Fighters should do more damage!
Looking at no feats
Sword and shield BM fighter with duelist
Monk with no subclass using flurry of blows
Level 1-5 monks do more damage than BM
Level 6-7 The classes do nearly identical damage
Level 8-10 monks do more damage
Level 11 the fighter finally pulls ahead and will stay ahead the rest of his career.
Level 11+ the monk has enough KI to flurry of blows all day and use stunning strike (gives party members advantage when used - which likely makes up the damage difference)
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On defenses,
The monk gets deflect missiles, evasion, stillness of mind, purity of body, diamond soul.
Fighters will get 1 hp extra per level up to level 8. The fighter will then get 2 extra hp per level. By level 12 he can get 3 extra hp per level
The fighter will have about 2 AC over the monk for most of his career.
The fighter has a slight edge IMO, but it's close.
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On, mobility
Monk wins handsdown
How much damage do you do when you can't reach the enemy? 0....
Is it ever effective to be able to prioritize high damage targets in the back of the enemies group? Monks can do this well.
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On control,
Monks win handsdown
It's not that you have to use stunning strike all the time, it's that having the option to use it allows you to pick the times it will be most efficient.
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On out of combat,
Depends on monk subclass but shadow monk makes an amazing option for this. Have I mentioned the base monk class is keeping up with the most damaging fighter subclass in damage? Yea, you can afford to pick any monk subclass you want.