Austin doesn't get hurricanes either. The tropical storms it gets have precipitation roughly equivalent to an atmospheric river. Austin gets snow once every two years, and it exceeded one inch only once since 2010. That amount of snow is hardly noticeable.
Another danger is cars getting swept away at low water crossings. You hear "turn around, don't drown" repeated a lot in Austin.
It is not at all unusual for people to get killed this way. They think their car can make it across, and they're wrong.
It's a problem in many parts of Texas because severe thunderstorms happen frequently and some of them bring heavy rain. But in Austin, it's especially bad because Austin is hilly, which makes flash floods worse.
Flooding on roads is not super common in Austin. Some areas have flooding, sure, but it’s extremely localized. I think you hear it a lot as outreach related to other Texas cities.
Houston, by comparison, might as well be a river for how often it floods and how widespread flooding tends to be there.