Disclaimer: I don't play Kali, and I've stopped playing support for them.
Kali's biggest strength seems to be in her mid-game. She does really well early game, but doesn't have the kill potential of dedicated early game champs (see Trist and Graves).
Mid game is when the roaming comes more into play (see sentinel), and team fights start occurring. Her ult initiation with another initiator (see malphite) of bloody brutal. And CC isn't as rampant mid-game as it is late, making her easier to peel.
Late game, she has to go against the hyper scaling of other ADC's and the assassin's itemization counters. And unfortunatly, she's so heavily dedicated to countering melee that she doesn't have the tools to deal with these other threats.
Really, she seems to fall into the same hole as other Utility ADC's. The current meta just doesn't support them.
I know this doesn't really help, but it's my perspective at least.
PS: My lack of support has nothing to do with viability. I just can't loose anymore windows to bad/troll Kali's in Yolo queue.
Her early game is pretty subpar. Her passive turns into a .5s self root with every auto. Her ability to dodge skillshots is pretty low also, since they can predict where she'll be. I completely agree on mid game, the point where items matter, and people don't have all of their abilities fully leveled. Late game, she dies to everyone. Assassins, mages, half the melees in the game can catch her. The other half can force her away from the fight. She's honestly weak right now, but people will be scared about buffs, since her kit looks amazing on paper.
Her saving grace is her ultimate. It has the potential to be one of the strongest ultimates in the game, up there with Rumbles and Morde's. I completely agree thou, yoloq Kalista usually ends up badly.
OP: Honestly, late game, you don't have cc or high damage. You spend the fight trying to be generally annoying to the other team, and helping whoever you soulbond to reposition. She honestly doesn't have what it takes to be useful late game.