A handful of observations (and I am an aeronautical engineer):
(1) Gyros are not inherently unsafe. What they are however is operated within a much less mature community than any other corner of aviation in the UK. So all of the constant dialogue between clever people about how to do things better or safer, does not happen in gyroplane flying to anything like the extent it does in fixed or conventional rotary, or even in balloons. This is really just a numbers game.
(2) For the same reasons, designs have not developed as far or as well as any other branch of aircraft design.
(3) However, they are improving. BCAR Section T, the UK airworthiness standard for gyroplanes, took a long time to bed in - but it has. Buy a type that is approved against Section T, or something that's simply been around for 20 years, and the assurance of safety is pretty good.
(4) However, , all of Piperboy's boxes are ticked better by a high performance flexwing microlight. Faster, cheaper, better performing in all but landing distance, and with a far better safety record than gyroplanes have: better than homebuilt light aeroplanes, and only marginally behind certified light aeroplanes. And joining a flying community more than 10 times the size of the gyroplane community.
For example:
Our Aircraft Range - P&M Aviation
Flylight Airsports Ltd. - Flexwing Microlights
The EclipseR 912 Raven Microlight
That said, gyroplanes fascinate me, and one of these days I'm going to go and learn to fly one. But that's speaking mostly as an inquisitive boffin who wants to understand them better, not a recreational pilot. In that capacity, I follow my own advice and have done a chunk of my leisure flying in a flexwing for years.
G