Does an Exemplar Brawler get any benefits from Close Weapon Mastery?

[Secret Wizard]

Quote:

At 5th level, a brawler's damage with close weapons increases. When wielding a close weapon, she uses the unarmed strike damage of a brawler 4 levels lower instead of the base damage for that weapon (for example, a 5th-level Medium brawler wielding a punching dagger deals 1d6 points of damage instead of the weapon's normal 1d4). If the weapon normally deals more damage than this, its damage is unchanged. This ability does not affect any other aspect of the weapon. The brawler can decide to use the weapon's base damage instead of her adjusted unarmed strike damage—this must be declared before the attack roll is made.

The Exemplar Brawler archetype loses Unarmed Strike, so its unarmed strike damage never increases... but once the Exemplar reaches 5th level, a brawler four levels lower, strictly speaking, would still have a large enough unarmed strike damage dice to replace dagger's base damage dice.

Is this reasoning correct?

[Driver 325 yards]

Yes. There are a lot of glitches in the new hybrid classes.

For instance, the brawler is proficient with shields as weapons but not as shields, which opens up the question of whether you can wield a shield as a weapon and declare that you are not using it as a shield.

For now, RAW, you are correct. It seems that glitches that add power to a character are the first to be fixed though. So have fun while you can.