Sending a Bitcoin (BTC) to a Bitcoin Cash (BCH, aka BCC) address in Kraken exch. without receiving the private key? Why cant Kraken simply receive full access to Alice account which she is willing to give. Kraken does not have to give Alice the private key. Kraken can create a wallet if that is really necessary or use a wallet that is already created which they have full access too, send the bitcoin to the wallet and then send it from the wallet to Alice BTC deposit account, give the Admin of Alice's Kraken account back to Alice's, therefore, No private key was given to Alice, security is still fully secure, Alice has the Bitcoin in her BTC account now. Alice pays Kraken for there services. Kraken is happy, Alice is happy. Why is this plan difficult?
Basically they don't have enough staff with security clearance to handle manual cross-chain recoveries. So only substantial amount will be considered. 


  It is Kraken's policy not to engage in efforts of recovery where BCH
  is sent to an XBT address or XBT is sent to a BCH address. Our last
  three blog posts have emphasized this point. Also, as you said,
  recovering your XBT funds will require manually handling the private
  keys associated to your BCH deposit address. Kraken has extensive
  security policies and procedures in place to ensure the safety of our
  customers' and our own funds. This means that the access to any
  private keys associated with any funds is extremely limited.


Source: https://www.reddit.com/r/btc/comments/6vpuy5/14_of_my_btc_held_in_limbo_at_kraken/