There is no difference between something happening automatically and invariably. Bankers are invariably selected for the House of Lords Chairs of the bank of zengland are invariably selected. Cof E bishops are automatically selected but are out at retirement.
For crying out loud Vlad - we've been through this. There is no equivalence between CofE bishops and bankers because:
1. There are no automatic places in the HoLs for bankers, there are automatic places for bishops.
2. For a banker to be given a seat they'd have to satisfy the standard nomination and appointment processes - bishops do not have to go through any HoLs appointment process - they automatically get a seat.
3. As far as I'm aware no serving Governor of the Bank of England (certainly in recent times) has ever had a seat in the HoLs and certainly didn't get one automatically when he was appointed. By contrast every ABoC (and other bishops) have been given an automatic seat in the HoL by virtue of being appointed to that role.
The only (near) equivalence is that some Governors of the Bank of England have been appointed to the HoL after they retired from the role - as far as I'm aware (and certain in recent times) all ABoC have been appointed (or rather re-appointed) to the HoL after they retired from the role.
The automatic seats for the bishops represents a special privilege for the CofE that no other organisation has.