I think we have to be more clear, POP, is the protocol for receiving emails, typically from your ISP mail account, where Apple have really cocked up with this upgrade (I have the same problem) is that this error also appears against sent mails that have attachments. They are sent to the outside world using SMTP, no copy is ever saved on a server, their time there is transient before being delivered to the recipient. The device where the email was composed is responsible for holding on to the original, something that my iPhone has previously done. Now I am missing several important emails.
Yes I know I can select "Always BCC myself" but that is something that I did not want to do and have never felt the need to do. As for POP not being designed to be used with several clients, I'm beg to differ, providing you decide to have one device as a "master" and therefore the only one to instruct the server to delete once downloaded, then it works just fine. It's something I've been using for at least 20 years!!!