Exponential search excels with unbounded arrays because: 1) Quickly finds relevant range, 2) Better than binary search for targets near start, 3) O(log i) complexity where i is target position, 4) Efficient for unknown or infinite arrays, 5) Minimizes unnecessary range scanning, 6) Combines benefits of linear and binary search, 7) Useful in streaming data scenarios, 8) Optimal for searching in unbounded search spaces.