“Yet the Tories have gambled, choosing a populist leader who is nobody’s idea of a safe pair of hands.”
What does it mean by saying “nobody’s idea of sth?”
Consider the opposite:
Dr. X is everybody‘s idea of a safe pair of hands
Consider a group of people and each has an idea, or image, in their mind of what a safe pair of hands looks/acts like. This description means that every person in the group agrees Dr. X fits every person’s idea of what a safe pair of hands looks like.
Dr. X is nobody‘s idea of a safe pair of hands
In your example, the exact opposite is true. Everyone in the group still has an idea in their mind, but this time Dr. X doesn’t fit any of those ideas.
This statement can acknowledge that there is diversity of opinion in a group, and yet not a single person thinks that Dr. X fits their individual opinion.