How can I add the Attachment field so it will be displayed underneath the To and CC fields when creating a new message? I have researched quite intensively but couldn't find any info.

By default the 'Attached' field will only be displayed below the To and CC fields when there is an attachment, attached to the message.

Unless there is an attachment, attached to the message there really is no use for this field. Also it allows you to notice at a glance if there is an attachment simply by the presence of the field.

There could be some sort of workaround such as an add-in or reg hack but I am not aware of such a thing, nor can I honestly think of any scenarios where this would be needed, but YMMV.