No, it's not that simple. Yes, you can migrate email to the new account and cut ties to the old account. Do you wish to have the migrated messages available online, that is, on the new account's server, so that you can access them via IMAP or webmail from any device?

I prefer to use a standard POP account. It looks like I can export just the mail separate from my profile tied to my old email address using Import Export Tools NG. Is this correct, and if so, can I import it into my new profile with the new address?

Since those messages are not part of the new account, I suggest importing them into Local Folders. You can then move them into the desired folder of the new account.

I prefer to use a standard POP account. It looks like I can export just the mail separate from my profile tied to my old email address using Import Export Tools NG. Is this correct, and if so, can I import it into my new profile with the new address?

That's correct, but you don't need a new Thunderbird profile to set up the new account in and to migrate email from the old account. Simply add the new account to the same Thunderbird profile, next to the old one, then you can migrate to your hearts content using the add-on, or directly by selecting multiple messages and moving or copying them over in small batches of about 2000 messages at a time.

Thanks for the assist!