Context
For a new campaign I'm building a protector aasimar kensei. We're using the Point Buy system, so being an unarmored monk I managed to raise my default AC to 15 (17 with Agile Parry), at level 3 through:
STR 10
DEX 15
CON 14
INT 8
WIS 16
CHA 10
At level 4 I was thinking of taking the Weapon Master feat, because I read online that it increases my Dexterity by 1, and lets me gain a fighting style from the fighter class. So, by picking the Mariner fighting style at level 4, I could raise my AC by 2 in just one level-up! This fighting style, from Unearthed Arcana: Waterborne Adventures, grants:
As long as you are not wearing heavy armor or using a shield, you have a swimming speed and a climbing speed equal to your normal speed, and you gain a +1 bonus to AC.
(Yes, the DM allows UA playtest material)
Now, unfortunately(!), we just discovered that according to the books Weapon Master actually doesn't let you pick a fighting style... The Player's Handbook states on page 170 about Weapon Master:
You have practiced extensively with a variety of weapons, gaining the following benefits:
Increase your Strength or Dexterity score by 1, to a maximum of 20.
You gain proficiency with four weapons of your choice. Each one must be a simple or martial weapon.
Discussion
Both the DM and myself agree that, by RAW, Weapon Master is rather underwhelming as a feat. So intuitively, the unofficial addition of the fighting style doesn't seem to be game-breaking to us. If anything, it makes the Weapon Master feat actually worthwhile in specific cases (instead of almost never really being worth taking it). I would say the improved Weapon Master would be comparable to the Magic Initiate feat, because by RAW the latter offers options to "obtain useful class features without multiclassing".
We think that taking a feat should be an investment worthy of not increasing ability scores with an additional point (especially when using the Point Buy system). However, we are unsure about how it could unbalance game play in ways we don't foresee right now.
Question
How would it unbalance game play to rule that Weapon Master allows for picking a fighting style, instead of four weapons?
To be clear, what does the DM need to keep in mind regarding encounter balance and player character options, when he allows the following emphasised addition to the feat:
You gain proficiency with four weapons of your choice. Each one must be a simple or martial weapon. Instead of gaining proficiency with four weapons, you may gain a fighting style of your choice from the fighter class.
A good answer addresses mechanical implications that makes this house-rule balanced or imbalanced: in comparison to how Weapon Master functions by RAW, and compared to other feats. A good answer addresses this in the context of our specific table.
An excellent answer also shares experience from a table that allows this house-rule, covers potential exploits and how it effects their game mechanically.
Possibly relevant details
I won't be the only melee combatant in this party, composition so far: barbarian, monk (me), war cleric, wizard.
We start at level 3. If our characters survive, we'll get to level 5 in just a few sessions (through milestones). After level 6 I'm seriously considering to multiclass into fighter, rogue or cleric. I plan to never wear any armor or a shield, so just wield the kensei weapons.
The DM wants this setting to be leaning towards a "Ragtag band of adventurers". He also prefers to keep mechanics balanced at the table, both for the players and him as DM. The campaign will be heavy on combat: we are holy crusaders.