Warlock themes, are to do with demons (specifically, the burning legion), fel magic (a breed of magic stemming in power from the burning legion), and a mastery of high-form magic (teleportation, pyromancy, etc) and in the case of affliction - they deal specifcially in spreading afflictions. The important thing to note, especcially in the case of Affliction (as it is the closest point of thematic overlap) is that Corruption or Unstable Affliction or Malefic Grasp or Drain Life / Soul - all of these are based in manifesting something essentially physical from the ether (Corrupting a target or afflicting them, draining them, grasping them, etc).
Destruction - being probably the furthest thematically from Shadow - is more akin to a Sorcerous Pyromancer - they are something along the lines of Fire Mages who - in their quest for still greater power - have begun dabbling in black magic. Demonology warlocks are very specifically thematically associated with the Burning Legion connection that warlocks all share - they transform into demons, they summon and command more powerful demons. The Affliction warlock is the closest thematically to a Warlock proper - but they are a far, far cry from being a Shadowpriest: what do I mean by a Shadowpriest then?
A Shadowpriest is, first and foremost, a Priest. We all began as priests - but - though our individual stories may differ - we became fascinated with the opposite of the Light. If "Know Your Enemy" is the first rule of war, Priests - who normally studiously study the Light - became a little too interested in the absence of light. That is why we are called "Shadow" priests, we are those priests who eschewed the light as we came to recognize that the true power to achieve our means came from knowing both sides of the coin, and then - when we have fully fallen - to going to whatever means necessary to achieve our ends. If you have heard the expression "When all you have is a hammer, every problem is a nail" - well, Shadowpriests were Priests, then Priests who knew Shadow magic, and then priests who decided the best way to heal their friends was to speak the word "Death" to those that would harm them (as a hammer to a defiant nail).
If you look at the spell set of the Spriest in particular (but also Priests in general) the power of the mind over the mind is far more important to us than the manipulation or manifestation of physical realities. We don't summon fire or demons or ice or teleport - all things I previously called high-form magic. All our spells deal with control over the mind - either ours or our opponents. Read these spell names out loud and think about the difference between a spell which manifests something physical (like a Chaos Bolt being a giant ball of fire) and something which is purely an abstraction of the mind:
Psychic Scream, Horror, Psyfiend
Mind Flay, Blast, Control, Bender
Silence, Shadow Word: Pain, Shadow Word: Death, Power Word: Shield
If I speak the word Pain, you feel it. If I say the word Death - and you are in a weakened state - you die - I didn't hit you in the face with a 12 foot sword, or immolate you in a wave of otherworldly fire - I merely told you that you were dead, and you believed me and stopped pumping your heart. Even spells like Inner Fire are a common reference to strong Willpower.
Ok, so shadowpriests are priests, who are particularly invested in the powers of the mind over itself and others - but what does this have to do with the Sha? The Sha are physical manifestations of emotions, in a very big and important way - a Sha is not actually there when you fight it - it's a construct - an idea - in your mind. It doesn't have internal organs, mama Sha's don't give birth to baby Sha's, Sha's do not die of old age. A priest - but a shadowpriest in particular - would have special interest in the ability of emotions to control, terrify, or empower their allies. The Sha of Anger, or Fear, or Despair - these are all manifestations of your mind: they are not demons. They are not even really high-form magic - but as you point out - they are something deeper, often more sinister but subtle. If a priest flays your mind, we do not whip out an egg beater and stir your brains around into mush - we discombobulate your thoughts (the flaying is metaphorical). Everything that a Spriest does, and everything that a Sha does - are fundamentally similar - we insert or subtract thoughts from your mind, we strip your will, we emit dread: but we don't throw fireballs or summon demons or huck fistfuls of virus and diseases at you.
The void - in wow lore or any other that I can think of - has Zero to do with wow-style warlocks. By its very definition, the Void is an absence - in WoW's case - of the Light. It is why we ourselves appear as nothing but a Shadow cast over anything we stand before, it is why our pets are similarly voids of light - fiends without physical form. Void tendrils aren't physical objects (despite Blizzards balance-based choice to make them punchable - presumably this represents mental struggle). Even the ability Void Shift - makes our health pools the opposite, just as we are opposite - antithesis of the Light. The idea of Void has infinitely more to do with Light than it does with Demonology, or Affliction, or Destruction - Void is practically a synonym for Shadow.
Now, if you wanted to talk about thematic overlap - the warlock spell Fear makes no sense for warlocks to have - that should be a priest spell. Conversely, Devouring Plague should be an Affliction spell - we spriests don't really have anything to do with diseases and plagues, that's warlock thing. I can explain why we have DP however, originally - DP was an Undead Priest-only spell (and it makes tons of sense for the Undead to have Devouring Plague), but then when it was overpowered - Blizzard gave it to all priests - then when they redesigned our class - they made it our finisher.
So, if you like - we can talk to the GMs and see if they will exchange Fear for Devouring Plague - on the grounds that it makes more sense thematically
Edit: Also would just like to point out, that Sha very clearly is a shortening of the word Shadow. As in Shadow of Anger, Shadow of Fear, Shadow of Despair - supported not only by their lore / stories / things they say - but also by the fact that they are giant swirling formless shadows. Also, when you get very close to a Sha - your world becomes grey and colourless - as though there wasn't very much Light present. The idea of the world becoming grey is also a common euphemism for severe depression (a psychological, but not physical - condition).