This antenna (and many others on the linked page) was evolved by NASA using a genetic algorithm. While highly effective, its design is counter-intuitive.
First, there is the potential of needing less power. Antenna ST5-3-10 achieves high gain (2-4dB) across a wider range of elevation angles. This allows a broader range of angles over which maximum data throughput can be achieved. Also, less power from the solar array and batteries may be required.
Second, the evolved antenna does not require a matching network nor a phasing circuit, removing two steps in design and fabrication of the antenna. A trivial transmission line may be used for the match on the flight antenna, but simulation results suggest that one is not required.
Third, the evolved antenna has more uniform coverage in that it has a uniform pattern with small ripples in the elevations of greatest interest (between 40 and 80 degrees). This allows for reliable performance as elevation angle relative to the ground changes.