Well, that's interesting. I have no idea what that means. Because again, I have an iPhone 4 and an iPad 1, and I have never had to set up a new iCloud email account on either of them in order to be able to use Notes.
Here's what I think is going on. Apple is doing a major revamp on iCloud security which will start on June 15 by requiring anyone who is using a 3rd party apps that access iCloud info to begin using App-specific passwords for those apps. Which in turn means that all of those people will have to set up Two-Factor Authentication in order to be able to continue to sign into those apps.
I have also seen the oddest things being asked for on my older devices when I sign out of iCloud and then back in again (which I am sure is directly related to Two-Factor Authentication security processes which I switched to from Two-Step a couple of days ago). When I sign back into iCloud on either my iPhone 4 or my iPad, it asks for my lock screen passcode for that device followed by asking me for my Mac User account passcode. Clearly ramped-up security (which is a good thing!).
So, either your original iCloud email address was compromised in some way, or it was being used by someone else, or Apple felt it was simply not a secure enough email address (for whatever reason). Since you are still only seeing your Apple ID and one iCloud email address on your Apple account, the new iCloud email address you set up appears to have replaced whatever was there before (which was likely the one you tried to use initially).
Of course, we have had no information about this, and it may not be an accurate conclusion, but since this type of issue does not happen with great regularity, it is not the "normal" way that it works.
Thanks for sticking with me on this. On this thread, I don't think we made a lot of progress over the years with this question. It was clearly an issue that was unique to a small percentage of people, but it simply did not seem logical. Don't know if what we are seeing now is even related to the original issues in 2012. Symptoms are the same, but the cause may be totally different.
But the takeaway here is that it does happen, and we at least know that sometimes people are going to have to set up a new iCloud email address for their Apple ID, most often when they try to turn on Notes on an older device.
So, again, thanks for working through it with me!
Cheers,
GB