I was under the impression that the Greeks leaned into a practice that was already well-established as part of rulership in the region. At the very least it seems we have evidence that Tutankhamun's parents were brother-sister and he appears to have had some severe abnormalities as a result:

> The results of the DNA analyses show that Tutankhamun was, beyond doubt, the child born from a first-degree brother-sister relationship between Akhenaten and Akhenaten’s sister (see Fig. 3). ... Pharaoh Tutankhamun suffered from congenital equinovarus deformity (also called ‘clubfoot’). The tomography scans of Tutankhamun’s mummy also revealed that the Pharaoh had a bone necrosis for quite a long time, which might have caused a walking disability. This was supported by the objects found next to his mummy. Did you know that 130 sticks and staves were found in its tomb?

https://blogs.ucl.ac.uk/researchers-in-museums/2018/08/16/co...