"Unable to authenticate" and Ban Appeal correspondence with Niantic

Is "Change Email" requirement useful for a PTC account?

I would like to give my experience regarding it when I started getting "unable to authenticate" error on an account botted using Pokefarmer. I had purchased this account online at lvl 33 and botted it to lvl 35. I dont want to type it out the whole correspondence so will copy paste my correspondence with Niantic.

pokemon-go-support@nianticlabs.com:

"I use PTC login and password to play pokemon go. PTC login is "_____". I have not been able to log into my PoGo account using my PTC id and password. It says "unable to authenticate". My trainer name is "_____" .
I would like to know the following.

Why am I getting "unable to authenticate" error on my PTC account when I try looging in PoGO? I tried all solutions out there, none of them seem to work.

1. Also, once I go to PTC login on Pokemon Go, and I put in the right password it says "unable to authenticate", If I put the wrong password is says "four attempts left before you will be locked out", I try again with wrong password, then it says "three attempts left", I put in the right password, then I get "unable to authenticate, please try again". Thereafter, I put in wrong password, the attempts are again reset to 4 and thus it says "four attempts left before you will be locked out". This is so frustrating!!!! I think the attempts get reset after I put in the right password, but there is something preventing me from logging in Pokemon Go. Why do you think this is happening?

2. Can you tell me if there is "_______" PTC account used to play pokemon go other than this. Ideally, there should not be as I have this account. And my email "_______@gmail.com" is associated with this PTC id, so why do you keep on asking me for the original email which was used to start playing pokemon go?"

Niantic's response:

"Sorry to hear you’re still having trouble logging into your account. We believe what you were experiencing was a temporary issue, and should be resolved.
Unfortunately, we're unable to find a Pokémon GO account associated with your email "___________@gmail.com."
Unfortunately, we're also unable to find a Pokémon GO Pokémon Trainer Club account associated with any of these Trainer nicknames: "___", "_____" "______"

It’s possible you created your Pokémon Trainer Club account with another email. Please note, while Pokémon Trainer Club allows you to change your email address on their website, this change will not be reflected in your Pokémon GO account. When contacting us about your account in the future, please include the original email as we require the correct email and nickname combination to verify ownership of your account and provide assistance."

To everyone wanting to change email to try and resolve future issues with Niantic, please note that "Change Email" option while buying accounts is not going to help.

Furthermore, when I asked if "unable to authenticate" would mean my account is banned, I got the follwing response.

"That is one possibility which I cannot confirm without your exact account email and nickname combination."

So, if you insist on buying Pokemon Go accounts with "change email" option, do keep this in mind.