In general you cannot drag an object that is already in your document into a Picture Frame by operating on the page. For example, if you Place a JPG file onto a page, then try to drag it onto a picture frame that is on the page, it won't work. You would have to Copy it, and then Paste as Content, or use the Layers panel. The intended use of Picture Frames is really via File > Place or the Place Image Tool, I think.,
Your experience with your Assets is at least consistent with these other cases.
I agree that it would be nice to be able to drag an Asset into a Picture Frame, and perhaps that's something that Serif will consider in the future. For now, you would need to use File > Place or the Place Image Tool, or drag it from an external Finder or File Explorer window, I think.