I found out how this works, with the new panel. To delete a mailbox that doesn't have an address associated anymore, you need to assign an address to it again before you can delete it. Then you can clean up the address afterwards:
Go to https://panel.dreamhost.com/index.cgi?tree=mail.addresses&
Edit a "forwarding-only address" to "also deliver to this mailbox" and specify the mailbox you want to delete. Click the save button (it's named Edit). The address now appears in the first part of the list, where addresses with mailboxes are listed.
Click "Del" to delete that address entirely, along with the mailbox you've just associated. You need to confirm this action.
When the mailbox is gone, you can re-create the address you just deleted, and just make it a forwarding-only address again. Now you've got the addresses back the way they were, and you deleted the mailbox.
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