There are messages I would rather not send — can they be switched off?

Yes, per message type, from the school's settings. A switched-off type is still recorded in the history as skipped, with a note saying who switched it off, rather than vanishing — so an admin never mistakes it for a failure.

A few types deliberately cannot be switched off by anyone: the Parents Portal and Teachers Portal PIN, number verification, notice that a school has been suspended, and the alert sent when the payout bank account is changed. The first three are credentials somebody is waiting on to sign in; the last is an alarm.