[D] Why do transformers use embeddings with the same dimensionality in each layer?

My intuition is that tokens get gradually enriched as we move through the layers, but that would mean we need to store a lot less information per token in the early layers than in the later ones.

Wouldn't it make sense to start out with (relatively) low-dimensional embeddings, and then project or extend these onto higher dimensions, until they reach their final size?

dimensionality embeddings information intuition layer low machinelearning mean per sense store through token tokens transformers