Perhaps exchange #1 could hold a database with bitcoin addresses and PGP-encrypted information about the bank accounts/mailing addresses of cryptocurrency holders.
Exchange #2 could hold the private keys of those bank/home details while receiving withdrawal requests and reimbursement for distributing bitcoin
The bitcoin holder can then request exchange #1 give a withdrawal request to exchange #2 in such a way that no exchange has enough information to connect a person to a bitcoin wallet.
Maybe I'm overthinking this; is there already a way that tech-savvy people can use Bitcoin in a way that's impossible to be tracked when converting to cash?