what is a private key? the memonic word, .... the password .... or the 16 pgrases word?
Private key can be found in Wallets & Addresses section of Blockchain account, but you could use that only in case you exported it before you lost your password and access to your account.
You should see your public address, balance and private key.
it is very intelligent, to set things in way, that if an user loose the private key , it may be recovered only accessing in the own account which is not possible to enter without password (that is lost )
it is evident, than an user not able to access own account, cannot get access to the private key
I think 3 things had to be done
1. inform previously users to export private keys,since it will not be possible to recover password because the private key
2. however making automatoic this exporting
2. inform users the 16 phrases word would be changed..
3. change the 16 phrases word with an intelligent way (of courseit is difficult for some programmers) for example taking 12 of those 16
but it is too difficult....too many neurons engaged