It would be good if there was more flexibility in the filename generated for binaries for certain schemas. In our case we want PDF downloads to not have the tcm uri appended, as this is a filename that is visible in the browser and that people will download to their local machine. In our case the PDF downloads all come from a system which already guarantees a unique filename, so its not necessary for Tridion/DXA to enforce additional uniqueness.

Similar to the recently added configuration for Embedding any type of component in RTF, the type of components to apply this functionality to could be controlled via a TBB parameter with a list of MM schema titles or namespaces: https://github.com/sdl/dxa-content-management/blob/891c89f4e2fd68238cf0db8426035968c74fb50d/Sdl.Web.Tridion.Templates.R2/Data/DataModelBuilderSettings.cs#L34

The DefaultModelBuilder and DataModelBuilder could then be altered where the call is to RenderedItem.AddBinary method (this has implementations which allow you to specify the filename).