I taxi my gyro with blades turning (it reduces stress on the head as you taxi over bumps)
It is possible to taxi too fast with the stick in the wrong place stall and wreck the gyro ... whilst taxiing. As I take off, if go to full power when the blades are not up to speed I will end up next to the runway in the middle of a pile of scrap metal.
Gyros have a high C of G and narrow under carridge, If I turn quickly after landing it will easily tip over and be wrecked. If a rotor blade travelling at about 300mph touches the ground the gyroplane will be wrecked.
both new and old Gyros are safe, you just need to know how to operate them.
and from a design point of view all flying machines that I have come across have their own design flaws that applies to both new and onld gyros, new and old fixed wing as well.