I'm definitely on both teams. We are sort of upside-down here in Florida as we grow annuals in winter for color, and they tend to peter out as soon as the nights get warm and the humidity returns. But I do take cuttings of anything I am particularly fond of, in the way of tender perennials (those that are generally used as annuals up north) because sometimes the same varieties are not offered the next year. Petunias actually do well from cuttings here, if I keep them in the shade and water sparingly through the muggy summers. They will jump up once the fall weather comes.
If cold weather threatens, and we do get occasional frosts even this far south, I take cuttings of any of my tender perennials like brugmansias, coleus and cane begonias. I don't have a greenhouse (hey, I live in a state-sized greenhouse most of the year) so I just bring the cuttings in through the cold nights, and start fresh plants once the weather stabilizes, usually in late February.