The airworthiness regulations specify functional requirements. They do not specify materials, form, etc. Thefore, the regulations in themselves do not prohibit innovation using new materials or construction techniques, so long as the final product meets the same functional safety requirements as any other design.
It is the manufacturer's responsibility to submit the required proof that a design meets the requirements. I'm not a "propeller guy" but for engines, there is usually a round of pre-certification discussion with the certifying authorities (e.g. the FAA or the equivalent in other countries) to agree exactly how the demonstration of will be carried out - for example whether by modelling and computer simulation, or by testing the finished product. In the case of computer simulation, this will include the method by which the software was verified (i.e. "how do you know that the software actually does what you think it does") and how the model was validated (i.e "how do you know if the model results are consistent with real life.")
The US certification requirements for propellers are Part 35 of the airworthiness regulations, and publicly available here.
Of course the entire process is carried out by humans, who are fallible. The regulations are often updated as a consequence of their failure - and not just for newsworthy major failures like the B787 battery fires of the B737-MAX problems.