I've found evidence that the OpenAI 1536D embeddings are unnecessairly big for 99% of use cases (and now there's a 3072D model?!) so the ability to reduce dimensionality directly from the API is appreciated for the reasons given in this post. Just chopping off dimensions to an arbitrary dimensionality is not a typical dimensionality reduction technique so that likely requires a special training/alignment technique that's novel.
EDIT: Tested the API: it does support reducing to an arbitrary number of dimensions other than the ones noted into the post. (even 2D for data viz, but may not be as useful since the embeddings are normalized)
The embeddings aren't "chopped off", the first components of the embedding will change as dimensionality reduces, but not much.