Permachase and permakite, as you call them, are actually central to her balance and kit in general. Notice that Kalista has a very inconsistent, teamwork-dependent steroid and poor damages on her abilities with the exception of a high stack count E. In order to stack up E that high, Kalista must have been fighting you for a long time; that's where the balance point comes in, similar to how Singed can't do lethal damage unless you chase him through poison for a long time. If you manage to escape or forced her to back out with your own damage, then her fully-backloaded E will do significantly less damage.
To top it off, Kalista's mobility is 100% combat-oriented and has no usability outside of combat. Notice how her. martial poise jumps have increased range when she's jumping away from you. That isn't just to help her escape , it's a counterplay mechanic as well. If Kalista is jumping away from you and you back out, Kalista has no way of getting back in on you unless she has another target she can attack.
In a sense, both of you have to "consent" to that long melee vs Kalista chase for it to happen. She signals that she wants to force the chase by jumping directly away from the fight. However, the chase doesn't happen unless you, the melee, choose to go for the chase. If you chase, you're essentially gambling that whatever tools you have will be able to halt and kill Kalista before she can rack up a lethal amount of E stacks. You have the ability to back out at any point, and if you back out while she keeps jumping away, she's out of the fight.
So clearly Kalista's optimal position for damage is right on the edges of the fight, darting around to avoid damage while dealing her own. However, by doing this, she puts herself at inherent risk due to her low range. Since she doesn't have the steroids of someone like Vayne to make up for that risk, she has no choice but to spec into that E with the Runaans to maximize her damage.
And that's where the brilliance in Kalista's design comes in: she's not really an AD carry in the truest sense of the word. AD carries have always been historically defined by their late game SINGLE TARGET DPS, yet Kalista doesn't really have it like other ADs do without proper coordination. She HAS to be dancing around the edge with Runaans, or she can't do enough damage to play the role!
The dashes will become less of the problem as people learn that Kalista is like Singed: don't chase. She's still overtuned right now, but her design shows great forethought and has much more counterplay then people will usually give it credit for.