Merge Intervals: is "sort first" the whole trick?

On Merge Intervals, sorting by start time makes everything else a single pass: you only ever compare each interval with the last merged one.

• Did you try to solve it before sorting? What went wrong?
• What other problems have you seen where "sort first, then scan" is the key?
• What is the most surprising input you tested? I would be interested in intervals that only touch at an endpoint, like [1,3] and [3,5].