I've seen in writing and on screen the phrase "but of course" used as a stand alone sentence. If one were to substitute just "of course" would the meaning change?
"Of course" is meant to be reassuring.
"But of course" is mildly demeaning, since it implies that the question did not deserve attention.
It may be acceptable when said by someone in authority to someone more junior in a family context, such as by a grandmother to a granddaughter. Outside of that context, as the people become less and less familiar (from neighbors to strangers, for example), or the relationship more regimented, it becomes more insulting.