I must admit that my fascination with gyros was initially sparked by Jay Carter's vertical jump Butterfly and the Carter Copter.
I followed their progress for a while, even put a deposit down for the proposed two seater... that never was. It was only later when Rusty Nance who test flew both revealed how poorly the Butterfly with the depleted uranium weights on it rotors handled, other than making spectacular leaps, that I realised that it was rather a one trick pony.
I have no doubt that it is possible, Dick and Carol's two machines seem to fly very well, but the fact that it has not yet become a staple gyrocopter feature would seem to indicate that it has it's downsides.
In general cost, weight, complexity, and reliability are all good reasons that more exotic features do not commonly/regularly appear on flying machines. That is not to say that these features cannot be achieved as each of those problems are over come.