Why can't I drag messages to folders on my Mac mini?

You can click a mail item, hold, and then drag to a folder location and release. That deposits it as an EML (.eml) Email message which Quick Look will allow you to read at that location. Double-clicking that icon will launch Mail and open that message in its own smaller window.

Because the Messages application was not designed with drag and drop support to the filesystem, not even as text clippings.