The gyro has received a bad rap, but the truth is, it's perhaps the safest aircraft in which you can fly. It needs almost no (and sometimes none) takeoff space, little landing space, and flies in a constant stateof autorotation. One needn't be concerned about losing an engine and transitioning to autorotation; you're already there. Low rotor inertia isn't an issue, nor is rotor RPM; once it's spinning and it's in flight, it takes care of itself without any pilot input.
Tail rotor issues are non issues because one isn't needed; torque isn't an issue. The gyro is almost intuitive in nature to fly; it's flown more like an airplane than a helicopter, and there's no collective to worry about or bury in an emergency.
Gyros got a bad rap over the years because for a long time, little existed in the way of any formal training; most all gyro operations were experimental, often build it yourself and learn to fly it yourself, at great peril. Lacking more modern understanding of light sport gyros, pusher gyros have often lacked any significant hoizontal stabilization. This, coupled with a traditionally significant offset between center of gravity, lift, and thrust, certain conditions could be achieved that lead to a "bunting" or power pushover...usually the result of a pilot induced oscillation. The results were often fatal.
Better training, better industry standardization (which is ongoing), closer regulation, support organizations such as the Popular Rotorcraft Association (and Ask First Society) have lead to vast improvements in safety, reliability, performance, design, etc. PRA has an FAA exemption to provide instruction in experimental gyros such as the Groen Brothers light offering...and a number of other safe and proven industry designs such as the Magni.
For most, tackling a gyro rating is for no other reason than personal satisfaction...but if you're so inclined, look into it. It's fun, it's safe, and like delving into any other area of aviation, it teaches you things about whatever it is that you do now that can only benifit you.