Personal feelings about alcohol aside, the real reason why SE has not directly allowed the player to be shown drinking but instead kind of sidestepped the subject (the mug emote is ambigious what is in it, and the same goes for the aforementioned times they've been offered drinks during cutscenes as well - the actual drink is not stated, but it's pretty clear to the player what it's meant to be), is due to laws requiring censorship around the depiction of alcohol in video games that exists in many countries, especially when it's interactive or part of gameplay to drink alcohol.
In such situations laws dictate a much higher and stricter rating of the game than what SE wants, as an important aspect of the game is it's accessability, despite the mature themes depicted in the game's story and setting. Considering these laws even precluded SE including a drink tumbler in the US Collector's Edition of FFXIV 1.0 (that was included in the JP and EU versions) - because they apparently ran afoul of certain US states' laws that fobid even drinking utensils being offered as promotions, SE's careful ambigious depiction of drinking and alcohol by the player's character in ARR makes sense, they don't want to run afoul of the law in multiple countries.