We are actively working on the reverse strategy in the context of the Orthanc project for medical imaging , namely to transparently convert DICOM to BIDS on-the-fly.
This way, the DICOM instances are considered as the primary data, and are always available if the series must be sent to another DICOM modality (for instance for radiological assessment as you mentioned). BIDS is secondary data that is transparently generated on demand. In our work, Orthanc is used as an extensible, open-source PACS server that can centralize images received from any DICOM modality. Raw data to be associated with a BIDS study are stored as attachments to the DICOM series.
A plugin for Orthanc named "orthanc-neuro" will soon be available as free and open-source software. In its first version, the plugin will allow to convert any DICOM series to NIfTI by calling a REST API. Future versions will introduce the configurable, automated conversion to BIDS.
The use of an Orthanc plugin allows to get rid of the "duct tape pipelines" by directly embedding the NIfTI/BIDS conversion into the core of a robust DICOM server.