Yes, this sounds like a joke about the olde worlde CEO who has his secretary print his emails, then transcribe his dictated replies. But printing message threads can be pretty useful. Lawyers, for example, may want a printed record, or a PDF, of a message thread. And even regular humans might appreciate a well-formatted archive of their messages that can be easily searched and marked up.
You still can’t do this on your iDevice. However, thanks to the amazing iMazing Mac app, you can quickly create PDFs of your messages, and even print them. Onto paper.