Don't worry about length, posts should be more like yours.
While I agree with you that
is in a tough spot, I disagree with the idea that he has no identity.
I believe his identity was clear when he used to build like an AD caster (Lucidity Boots, Manamune, Yomumu's, Last Whisper, Maw). The only "weird" part of his kit was his Passive, which provided Attack Speed to a character that snipes you from 1000+ Range.
Due to targeted nerfs at his Q, the change to Last Whisper and somewhat delayed effectivenes of Lethality (compared to Armor Pen) it resulted in the loss of his unique build and Play Style. He was a Supportive AD Sniper that provided lots of poke damage, utility and waveclear, and had high DPS in teamfights through his abilities. He brings advantages that Jayce and Ezreal would dream to have.
Here I comment a bit about your list:
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Imo, Varus has better AD scalings than Kai'sa and he has them on his basic long Range abilities, while Kai'sa has on a close target nuke (and her Ultimate shield). I can't talk about their AP scaling, as I'm not entirely accustomed to them. I agree with you that she has more reliable Damage.
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Range, CD and Damage aren't the only factors in deciding the effectiveness of a Poke ability. The piercing effect is pretty much invaluable, as most tanks would simply absorb your ability, taking little to no damage compared to a carry. In teamfights it is much more valuable to have an AoE ability than a one-target skillshot nuke, unless you catch a carry out of position. Second thing is missle speed. Varus Q is one one the fastest skillshots in the game, making his poke incredibly reliable by giving the opponents little time to react. Shooting behind walls or bushes leads to an almost invisible arrow for the opponent. That is the main reason why I think Riot nerfed his Full-AD build.
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I totally agree. I hope that his new W active and the comeback of Last Whisper will at least make AD Varus viable.
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While indirectly, Varus does have synergy with CC monsters. His abilities deal a ton of damage when landing, and after 6, he and his support will murder you. I remember people playing in season 3 Varus with Leona bot and they were literally a kill lane.
I agree with the negatives, the only thing I would add is that only her W is long ranged and that she has lower AA Range than most champions, making her susceptible to long Range Poke. In contrast, Varus has higher than average Range and all his abilities are long Ranged, making him pretty safe in this department.
Overall, I believe Kai'sa is simply better than current Varus because both of them depend on their AAs too much. I believe Riot should look at his kit and try to further enchant his niche of an AD Caster.