I use POP3 for some services. I have one mailbox that I share with my wife as a joint household e-mail address (we both also have personal addresses). Having syncing between devices would be a nightmare as things would get marked read by the other person. Yes, I could set it up to forward to our personal mailboxes, but it's been working fine for 20 years, so why change.
More importantly with POP - you mail gets downloaded to your device and then that's it. It's yours, secure, for you to manage. With IMAP there's always the possibility of the ISPs server hiccuping and deleting mail off your machine that you thought you had safely downloaded.
Even with IMAP, you can secure messages by moving them to local folders. And with multiple devices, you can move a different set of messages to each device. You can also move messages back to the inbox, in order to share with another device.
I used to be a POP fanatic, mostly because I didn't like the idea of leaving copies on the server. But then, the NSA probably logs everything, so hey.
More importantly with POP - you mail gets downloaded to your device and then that's it. It's yours, secure, for you to manage. With IMAP there's always the possibility of the ISPs server hiccuping and deleting mail off your machine that you thought you had safely downloaded.