They'd already placed the tire onto a new wheel rim when I got there so it was ready to go. I said I could carry it out myself. It wouldn't have been a problem. But they insisted on driving my car into the service bay so that someone could put it into the trunk. Then they drove it back out to the front. Peculiar, but it's probably the service protocol.
Anyway, I don't know why I never thought of this before. If I got a flat, changing to the full-sized tire would allow me to drive home and take care of the flat the next day at my convenience. The little donut tire goes for about 20 miles and then goes flat itself. And here's the kicker: The donut tire costs more than the full-sized tire! So what's the point of it? I guess sometimes the problem needs to come up before I see the better way.