I've decided to create a concise list of lore and story direction grievances most often brought up by players of both factions. Please note: this is NOT a pissing contest to see which side has it worst, as I will try to illustrate that BOTH sides have their own problems.
Alliance:
1. Victimization: The Alliance from late Wrath/early Cata onward has felt constantly victimized, taking the brunt of major defeats and humiliation at the hands of the Horde with little to show for it besides some hollow notion of moral superiority. From the Broken Front, to Gilneas and Ashenvale being ravaged by the Horde in Cata, to the utter defeat and destruction at Theramore and now Teldrassil, the Alliance feels it like its lands, peoples, and civilizations are being torn down for cheap shock value. Races like the Worgen and now Night Elves feel humiliated, demoralized, and displaced from the lands and lore that made them worth playing. Even so-called "revenge" plots feel hollow and half-assed as victims fail to bring any semblance of justice upon perpetrators, as seen when Thrall killed Garrosh and the even more pathetic attempt to stop Nathanos by the supposedly "powered up" night elves.
2. Reactionary and Passive: The Alliance lacks almost any kind of agency regarding the plot. Constantly acting in response to the Horde and other forces of the narrative. There was an opportunity for the Alliance to take the initiative and start the war proper in BFA, and indeed many Alliance players voiced a willingness to strike first even if to do so would be morally dubious. (more on that later) But it seems Blizzard is dead-set on maintaining the status quo of "Horde acts, Alliance reacts" even to the point of absurdity. When you observe the motivations of some of our chief characters like Jaina and previously, Varian, you see that they rarely if ever act as a pro-active force in the narrative, initiating events.
3. Lawful Goodness to the point of stupidity: drawing on the first 2 points, it seems Blizzard is absolutely resolved on making the Alliance the "Lawful Good" or rather the Lawful Stupid faction. The Alliance blunders into colossal defeats (Theramore, War of Thorns) that boggle suspension of belief, but more than that, the Alliance is written as ever righteous and forgiving, especially regarding the Horde's crimes. In a position of total advantage after the Siege of Orgrimmar, the Alliance gives up its advantage and gives a laughably hollow threat. In BFA it seems the Alliance is already poised to forgive and forget the mass murder of civilians during the War of Thorns and the rest of the Horde's involvement for apparently no other reason beyond being the designated morally righteous faction. This is not believable in any sense of the word.
4. Not an Alliance anymore, now a horribly written and contrived Human Empire: The Alliance used to pride itself on being an actual Alliance, now it is a Human Empire, one of the most boring and badly written Empires in fantasy. The position of "High King" should never have been a thing. It seems to be cooked up to facilitate more lazy storytelling. When a ruler of one nation state in a mutual coalition possesses absolute military authority and enforces his will on the others, he ceases to be the leader of one nation and becomes an Emperor in all but name. This "Blue Warchief" position robs the Alliance of its core identity, and creates absurd scenarios where young Human kings dictate over Dwarves and Gnomes with centuries of experience, or in the case of Draenei and Night Elves, millennia. There is a position of supreme military authority, Supreme Allied Commander, held by Lothar and Turalyon respectively, but both of those men were chosen for their military experience and due to their apolitical positions as a disposed Knight of a fallen kingdom and a Holy Man respectively.