Why would notes have to be tied to email? Email is for e emailing...? Still don't get that.
Notes do not have to be tied to email. But if you want to synchronize notes across devices, you need to have some way to pass the changes back and forth. That means you have to have a server somewhere that all the devices talk to, and everyone needs to set up a secure account on that server so that my notes and your notes don't get intermixed.
Email is for emailing, but what is emailing? Emailing is a way to send messages from one place to another. And what's a message? Just data.
Email is ubiquitous. Pretty much everyone already has one or more email accounts, already all set up. That means everyone already has a secure personal account, probably more than one, that can be used to exchange data. That's exactly what we need in order to synchronize notes. Why re-create a system that's already in place?
What happens is that if you make a change in a note on one device, as soon as you tap "Done" the changes are sent as a specially formatted email message to your IMAP account. All other devices that can access that IMAP account will notice the message, and use it to update their copy of the note.
I don't know the details, but I assume part of the "special formatting" is that they're placed in a mailbox that Mail.app knows is for notes. Either it passes the messages along to the Notes app, or more likely ignores them and lets Notes.app access the IMAP account directly. Either way, you will never see these messages in your INBOX.
Apple has complete control of your iCloud email account, and can do this very efficiently there. That lets them use this mechanism to synchronize much more than just Notes.
The advantage of being able to use a non-iCloud account is that you can then share the notes with a wider circle of other people. You can create a shopping list note that all members of your household can edit, and the changes are immediately visible to whomever is at the store doing the actual shopping.
Or a small business can set up an email account just for this purpose, and give everyone in the company access to it. Then they all see the same notes, updated in more-or-less real time. They can even configure the email account so that it's used only for notes, and never for ordinary mail. (In Settings→Mail, Contacts, Calendars, turn on Notes but turn off Mail for that account.)
In both cases, the devices that share the note are not limited to devices that share the same AppleID. You can easily configure the extent of the sharing as narrowly or as broadly as you want.
The narrowest sharing is notes you that don't want to share at all. Associate them with the artificial account named "On My iPhone". For those notes, there is no email involved.
