File Viewer doesn't upload to SiteAssets

I think we are in agreement here - the uploader should have a choice! But your scenario is exactly why I recommend uploading first, to an organized and manageable location in the Documents library or another document library or even a folder within a library - and then creating a link in appropriate places. The same document is often referenced in multiple contexts on different pages. Following an "upload first" approach helps to ensure that there is one source of truth for the document, no matter where it is referenced. Since the automatically created sub-folders in Site Assets are page-specific, this could create an opportunity for multiple versions of the same document to get uploaded on different pages. This may not be the case for your specific use case, but as a general rule, I find this approach is much easier from a training and content management perspective. If it were possible to choose on upload, I would still recommend not storing documents in Site Assets for that reason.