A Fighting style is worth 2 cantrips. That's what Divine Warrior and Druidic Warrior tell us. That means a single Fighting Style is worth less than Magic Initiate.
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I don't know why adding Fighting Style to a Magic User is any worse than adding Magic Initiate to a Martial class.
Well, you cannot weight Fighting Style like that. First of all, Divine/Druidic Warrior alternate features aren't confirmed yet. Second, it is possible for competitive options in the game to have an asymmetric cost, in the sense that giving up something in exchange for something else might be costly in both directions i.e. you give up more that you get in exchange, so just because giving up a Fighting Style might end up granting 2 cantrips, it doesn't mean it is fair from someone else to give up 2 cantrips and get a Fighting Style.
That said, I have probably overreacted in worrying about balance of granting a Fighting Style with a feat. Generally speaking, there are feats which grant bigger average bonuses than Fighting Styles. In addition, spellcasters aren't going to get the benefits from a Fighting Style as often as a Fighter would, because typically they're going to spend many rounds casting spells instead of attacking; defense is the only Style which they will benefit from all the time, but +1 AC ain't gonna break the game. So basically only Rogues are really going to get a weapon Style benefit on all rounds, but again +2 damage/turn from Archery or Duelist is not gamebreaking.
That leaves a Rogue taking the 2WF Style the only possible combination that is a bit too good. The Dual Wielder feat gives +1 (average) or +2 (max) damage per turn (by upgrading your off-hand weapon from d6 to d8) and an extra +1 AC. The 2WF Style grants potentially +5 damage per turn, when you max your Dex, it's definitely better although I can still see the appeal of that AC bonus for rogues.
So it's really just one case that leaves me skeptic, but the others will be fine.
There is still the issue with diminishing the uniqueness of classes, particularly the Fighter (a trend that always surfaces at some point in every edition), but I understand that few people besides me still care about this.