Most interval problems follow this pattern:
Sort: by start time (for merging) or end time (for selection)
Scan: left to right, maintaining state
Decide: at each interval: merge, extend, or start new
Without sorting first, you would need comparisons to check all pairs. Sorting lets you process intervals in order, making local decisions that lead to global optimality. The pattern runs in time (sorting) and typically space if done in-place.