When you remove a POP email account from the Apple Mail app, the account's email messages are removed from your Mac. However, copies of these messages will remain on the mail server and can still be accessed through webmail or other email clients.
I don't think this is accurate. What you're describing sounds a lot more like how IMAP works: it
mirrors what's on the email server and downloads copies. What's stored on the Mac is also stored on the server, so there are no issues if you log in with multiple devices.
POP, on the other hand,
fetches emails from the server and (if I'm remembering correctly) either deletes them from the server or leaves the originals there, depending on how the email client is configured. POP is an older standard that dates back to the days when an end user wasn't likely to have much server-side storage, so it was designed to just pass along email to its end storage destination of the user's local hard drive.
In any case, the safest course of action is -- as you say -- to copy all emails to an On My Mac folder.