The account settings UI is counterintuitive in this regard. The sender addresses section shows the comment 'Validate an individual addresses to track campaign statistics by sender address.', but it turns out that adding individual sender addresses is required to send any template. I expected to be able to enter a random sender address under one of my validated domains, but that is not possible. Allowing this would be my preferred solution of course, but I imagine that can be quite invasive, so please just clarify that an individual sender address is required instead.