There's a simpler explanation for why Intel used AMD GPUs for a while: Intel's new integrated GPU design couldn't ship until they sorted out their 10nm issues, and their older design wasn't competitive. When Intel went shopping for GPUs on the open market, they could get them cheaper from AMD than Nvidia (though the HBM2 requirement was a clear downside). They actually paired AMD GPUs with both 14nm Kaby Lake and their failed 10nm Cannon Lake processors that had broken integrated GPUs. The short-lived Intel/AMD GPU partnership came to an end because Nvidia's lead over AMD got too big, but it was doomed to be cancelled as soon as Intel gets 10nm working.

What is Nvidia's lead over AMD? Intel's non-AMD gpus are Intel gpus

Do Nvidia integrated gpu (mpgu) exist?

Nnvidia claims they exist but all their weblinks to details are dead. https://www.nvidia.com/object/main_mobo_gpus.html

Nvidia and AMD both make discrete mobile GPUs, and those are the only two options for offering better GPU performance on an Intel laptop when Intel's own GPU is inadequate. Nvidia's GPUs have for years generally had a substantial power efficiency over AMD's.