Does anybody know why POP3 doesn't synchronize the read status and the folder-categorization of emails?
And if there's no good reason for that: why hasn't POP3 been changed yet?
POP stands for Post Office Protocol.
The protocol was the first standard for email delivery where mail is being viewed from the eyes of the postman. The protocol dictates that it will deliver mail from the server to you and your email client will download the mail. If your client states that it already has this copy of the email, it will reject that said copy. Usually, the client will delete email from the server after a while and keep the local copy to save diskspace.
Other than that, the POP3 protocol doesn't do.
Why hasn't POP3 changed? Because any change would mean older clients would no longer function properly. So instead, IMAP (Internet Message Access Protocol) was created. Instead of just delivering the email to your email client, IMAP will actually synchronize its status too, though with IMAP, mail is stored on the server permanently, until deleted. Any server that supports POP3 will also support IMAP.
So basically, to sum it up: the reason is, it was developed, but renamed for backwards compatibility.
You will find that when you configure your email, you can choose between POP3 and IMAP.
Do note, the biggest difference between POP3 and IMAP, is that IMAP will store mail on the server, and upon deleting a mail, it will be both deleted from the client and server. POP3 will download the mail, and if configured, the mail will automatically be deleted from the server, but never automatically from the client. This means, that the server does not need a lot of diskspace to save your email, something that was very expensive back in the day.