Been tuning up what I consider a best-case Khan & Birds system. It's actually produced a "shapery" rig with lots of actions that is quite fun to play. In this process, I've discovered perhaps Khan's biggest disadvantage. To articulate it, I'd like to describe what I think is Khan's ultimate board state--one that takes quite some time and credits to set up, but can be reliably achieved if the Corp isn't hyper-diligent in checking the runner's early-game run economy. Here's a link to the deck. I know, I's really an Andy rebirth deck. Sorry.

The strategy is to set up a board state where rezzing ICE hits the Corp's bank harder than it hits Khan's, even after multiple runs. That's not how ICE is supposed to work for the Corp. Her "Vamp" rig includes 1) the GPS Breaker Birds, 2) Autoscripter, 3) Sahasrara 4) Temüjin Contract. When Khan breaks the ICE, she can pay 2 creds to derez, bouncing the Bird to the runners grip. Immediately, Khan can reinstall the Bird for free using her ability and Sahasrara credits, while gaining a click with Autoscripter. Upon successful run Khan gains credits from Temüjin to fund the next run. If Khan is already ahead in credits, the Corp may refuse to self-Vamp and not rez the ICE at all. This easy access can be used to lock HQ and sometimes gain enough credits for an R&D run each turn.

Here's the catch. Khan's ID only triggers the first time you pass a piece of ice each turn. All the Corp needs to neutralize this threat is to install a cheap ICE like Vanilla or Quandary above a piece of more expensive ICE. Then re-rezzing the first piece of ICE is cheap/free for the Corp and the entire threat is neutralized. Khan's ability is thus reduced to only gaining a click, but at a cost of 3 creds with a Bird Breaker. It ain't worth it. En Passant could be a good counter measure, but at 2 influence it is hard to justify in a strategy that is already needs so many economy and tech cards.

A strategy that requires so much investment, but is so easily neutralized...welp, it's just not that great. Moreover, a lot of great Corp decks use only light ICE. For those decks, you wouldn't want to use Khan's inefficient Birds at all and should probably rely on an AI breaker. For Khan's ability to really be worthwhile, it would need to be once per turn when you pass a piece of ICE rather than the first time you pass a piece of ICE. Perhaps it would even need to be once per run to be considered competitive given the setup investment, heavy economy requirement, and inefficiency of the Breaker Birds.

Still, Khan has a cool, interactive mechanic that can occasionally set up a devastating late game. She is fun to play, and I can't seem to give up on her.

I like her a lot. She is just super fun to use, though challenging. —
I wouldn't say that the threat is neutralised by using cheap ICE as the first piece of ICE you pass each turn, you just need to have two sets of birds. Take the case of a server with Vanilla and Tollbooth and all Birds installed. You pass the Vanilla, install a second Peregrine, then bounce one of the Peregrines during the derez. This is memory intensive, but Gauntlet and using Cybsoft MacroDrives instead of Sahasraras allows it. —
@manicmoleman Thx for the great insight. I do have two sets of Birds so I will try this. I tried Cybsoft drives but they just didn't help enough for the initial Bird installs. One Sahasrara goes a long way in installing the programs while struggling for early economy. When I first saw Gauntlet, I balked at the cost. But after a second look, it would allow me to ditch an HQ interface and swap it for a Pheromones. Might even try two-for-two!! Thanks for your reply! —
No worries! I, too, am a little bit obsessed with making Khan 'work'. In my current build I'm spending influence on 2 Magnum Opera to fund the Birds and using Datasuckers to deal with awkward ICE. Having a Magnum Opus on the board really helps with when the Corp has locked you out of your Temujin server. —
I have also begun playing with this build a little. Have you considered adding a compromised employee or two to the mix? If you're bouncing ice and getting the corp to re-rez, this helps some more. I've had very bad econ draw the couple times I've tried it. One game I had one one econ card in the first 18 draws. —