It is acknowledged fact that uncertificated aircraft are no less "safe" than certificated aircraft..
This door swings both ways....
No matter which way you look at it, a certified aircraft has demonstrated compliance to all of the applicable certification requirements. A non certified aircraft may meet some, or perhaps all of those requirements (or maybe few) but it's compliance status is not clearly defined. Therefore, if the "public", and pilots are content to fly in aircraft which have not been found to comply with design requirements, and later quality of maintenance, they are well able to fly non certified - but generally not for rent nor hire.
Our respective societies still feel the need (like it or not) to assure that aircraft being operated for hire, or internationally, in most cases, comply with nationally accepted design requirements. I have lobbied the regulators for years to develop a simplified regulatory path for these aircraft, and even a regulator agrees that it is past due. It's just the inertia to start that regulatory shift - and toward what?
ASTM was a big step forward, but it still has roots in the formal certification standards. There are many excellent non certified aircraft out there, and I think that some would largely comply were they to be submitted for acceptance. However, "the public" still want aircraft with predictable characteristics, so they are not let down the once a year they fly, and not going to have one drop on them the rest of the time.
There is a huge paperwork exercise associated with any certification, because the certifying authority wants records on file, in case they end up in court a decade from now....