Embrace the Void
It isn't even fair to say that Legacy of the Void's terrible storytelling is handicapped by the fact that the protoss, as a race, are designed explicitly for us mere humans to have difficulty empathizing with. That they don't have mouths, tend to speak in a businesslike way, and walk around adorned with wacky-looking ornate bullshit -- none of this stopped the campaign's most interesting character, a Tal'darim protoss named Alarak, from stealing the show every time he appeared in it.
Void's underwhelming, hackneyed plot is really just another indictment in Blizzard's last several years of not caring about any of the substance behind its lavish cutscenes. In lieu of interesting new ideas, they keep trying to explain the mysteries behind the old ideas - the Horadrim, the xel'naga, what have you - which only ruins the existing lore's mystique.
But I digress. You shouldn't care about Void's stupid story -- because the campaign missions are, as in Wings and Swarm, generally well-crafted and exciting. Aside from the last couple, which get really fucking annoying, there are some creatively satisfying objectives and mechanics to play with here. Particularly memorable are the on-foot missions that have you controlling multiple hero units, managing their superpower abilities in tandem.
And as before, progression through the campaign brings unit upgrades that both call back to classic content and introduce brand new abilities. The Tal'darim Void Ray, for example, fires multiple beams at multiple targets. It is hype.
I may not give a shit about Amon or whatever, but Legacy of the Void gave me several evenings' worth of fun missions to play through, and that's pretty good.
Better than: Mechanically and architecturally, both Wings of Liberty and Heart of the Swarm
Not as good as: Narratively, both Wings of Liberty and Heart of the Swarm
It's a shame: that Grey Goo, which had a really engaging aliens-at-war story from what I saw, couldn't have been more fun to play.
Progress: Finished the campaign and epilogue.