On the other hand, you are screwed when that one train gets cancelled, or when you miss it because you slept through your alarm clock. And because you can't control its schedule, you are on average 45 minutes early at your office.

For practical use one train every 30 minutes is what I would consider the bare minimum, and one train every 15 minutes is when I would be willing to rely on it for day-to-day use. I'm fine with low-frequency trains when I am going on holiday and will be spending the entire day traveling anyways, but it's just not good enough as daily transport.