Firstly, even for non vector data, read/write transactional database vs read-optimized store purely for fast serving are already markedly different. Then, the shape of data that is used to generate embeddings is markedly different than the shape of data that is ready to transact or serve.
So, no matter where it is stored, it has to leave that store, get transformed and enriched and then run through an embeddings generator (ML inference).
Then, it has to be stored in a manner that is optimal for retrieval ranking. If you are doing ANN that's one thing, but if you are doing attribute based filtering while retrieving and you wish to accelerate it through GPU to do more exhaustive search, that's another thing altogether.
All these lead to fairly sophisticated optimized implementation. Sure, a singular database product solution that has all these different optimized engines can emerge over time but surely it is too early today to converge like this.