Face API allows has 2 different face detection model.
The main difference (at least for us) is that detection_01 provides face attributes, while detection_02 does not, but it detects small, side-view and blurry faces.

We would be keen to use AnalyzeImage with detection_02 - we don't need face attributes but need to find as many faces as possible along with other objects and image description.

It's possible to do it now by making separate calls to AnalyzeImage and Face.DetectFaces, but it's not very good cost wise.

Would it be possible to extend AnalyzeImage API to allow setting face detection model?

The difference between the face detection models can be found here https://docs.microsoft.com/en-us/azure/cognitive-services/face/face-api-how-to-topics/specify-detection-model#evaluate-different-models.