Q: Cannot unlink old e-mail account from iCloud

I am trying to update my iCloud e-mail address to reflect my new e-mail, however there is no way on my iPad to do this -- it refuses to take my old password and even though I have reset my password with Apple AND provided both my old and new e-mail addresses and entered all of the correct verification questions it persists in asking me for the password for my old e-mail account. This is an AMAZINGLY FRUSTRATING process Apple has set it -- it has virtually no comparison to any other security system online -- my bank, my brokerage account, my access to my health records are ALL SIGNIFICANTLY EASIER TO ACCESS and to manage security for. You guys HAVE to make this easier and more intuitive. It's 100% a broken system right now -- what's the point of having verification questions and asking for both old and new e-mail accounts if this does NOTHING but put you back in the same inescapable loop? For the amount of money you guys make off your devices and digital sales you'd think you could hire someone to solve issues like this gracefully. PLEASE help resolve this. I am highly technically literate...I cannot imagine what it might be like for your users who are less so.