That's not a balance issue.
How is it not a balance issue? What meaning does 1/4 vs 1 have, if it's not about relative power of the ability? You were talking in-world justifications. In-world justifications are just as important whether it's 1/4 an action, or a full action, right? In fact, you said as much earlier. It's only power/balance that is a difference there. It's the issue you raised, why don't you explain?
Except for rules lawyering, there's no reason you could not opportunity attack a friendly creature
It's not rules lawyering. There's nothing hazy about the rule, you're not interpreting the rule in some favorable manner or something, the rule is utterly clear and nobody has ever expressed any doubts about it. That's not rules lawyering, it's just a rule. The rule is you only get an opportunity attack if it's a hostile creature leaving your threatened space, not for an ally.
And yes, if it could apply to allies, it would sometimes be beneficial, particularly when combined with some charm type spells on monsters who would not only be attacking an ally for that round (per the spell) but might then be attacking their allies (though the spell doesn't specify that), and I think it might have some issues with some feats as well, grappling an ally when they leave your threatened space because you're preventing them from heading into a trap you know about and they do not, etc... Again, the focus of this isn't "who can I attack with an opportunity attack", it's "when is an opportunity attack triggered". They don't trigger for allies leaving your threatened area. What is your in-world explanation for why that is, and what will you say when your players ask about it?
The rule says "hostile" because that's the common case. I don't think the word is a significant crunch restriction.
No it says hostile because that's the rule, it's EVERYWHERE in the rules (I quoted a half dozen, I could easily quote a dozen), and it's intentional and related to what the designers encountered in some prior editions where they didn't carve out that design space and some things functioned wonky because of it. In fact, why don't you ask Crawford or Mearls about it - I feel quite sure they will confirm it was intentional and not just a "common" case but because they don't want those things functioning against allies for a variety of reasons. Crunch reasons. Balance reasons. Flavor reasons. Many reasons.
I'm done in this thread unless new voices speak up with new questions.
OK, that's cool. For what it is worth, if you decide later to come back, I still genuinely do want to know why opportunity attacks only trigger when a hostile creature leaves your threatened space in your game, OR why 1/4 action vs 1 action is relevant if it's not an issue of balance. These seem like questions that help inform your decision on the feat in question.