The question "Why not a V-tail?" is better flipped on its head: "Why do it?" Always start with majority, proven methods and only go elsewhere if you can improve on them. IOW, don't re-invent the wheel.
The V-tail was a design fad decades ago, when it made its way into the Bonanza -- a fast, expensive plane for its time. The theory then was that each joint between the fuselage and a wing or tail surface produce a bit of drag -- and two joints made less drag than three. The gains even for a slick FW plane were marginal at best. In a gyro, which has the aerodynamics of a Port-A-Potty -- any possible gain is overwhelmed by the enormous drag of everything else -- especially the rotor itself.
The V-tail is more challenging to design and build, especially when attached to a slender tube such as the typical gyro tail tube. The "ruddervators" will produce a certain amount of adverse aileron effect when activated: e.g. rudder applied for a left yaw will also create right roll (so will an ordinary rudder, but not as much). This sets up a slip, requiring left stick. Who needs that complication? Some gyro designs do not tolerate slips very well at high speeds and throttle settings.