Why do autogyros exist?
Autogyro blades have a higher airspeed than the aircraft that is carrying them, so they can generate lift even when the aircraft speed is low. They fly as if they had a wing the size of the whole disk, not just the blade area - yet can be stored or transported easily.

They can land (but not take off) almost vertically, which is a useful safety feature in the event of an engine failure.

Having said that, they aren't common because they don't do anything useful significantly better than the other options, except perhaps being 'different and interesting'. Flying slowly isn't terribly useful.