If you want to download from the data source as a csv without going into a workbook I think the only way to do it currently is via Tableau Desktop by connecting to the published data source and selecting "Data -> Export to CSV"
Currently in Tableau if you select the download data source option in your browser is will download as a .tdsx/.tds file. There is no export data source option currently but it might be something to bring up in the ideas forum.
The other alternative I think you are aware of would be if the data source is connected to a workbook that you would select the "Download" option in the workbook and choose to download a csv file
Hope this helps,
Perhaps creating dashboards from them is my only real option. I'd hoped to avoid this but I can't really see a way around it.