When I move a message from one account to another (by dragging, or "Move to"), or to a local folder, I expect the message to be deleted on the original account. However, what Apple Mail does is archiving the original message. Is it possible to realize my desired behavior (e.g., via a rule or a script)?
Archive is a misnomer on Apple Mail.
It is not Archived.
It is actually the Goggles "All Mail" folder.
If you do not want to see it in your Apple Mail disable it in Google Mail.
Google will keep all your emails in it.
It would only possibly work if the mail accounts were POP accounts and you had your server settings configured to delete messages from the server when read. Most mail accounts now use IMAP which use different behaviors for message storage, both on the server and in the email clients.
You could structure some Rules in Mail to accomplish what you're trying to do.