It might be a bug related to tdf#112972 .
I can see the image in FreeClipboard Viewer as Bitmap DIB and I can paste from Windows History into Word and into graphics programs.
Personally, I always try to Import the image in a finished size, compression and format so I can export as pdf with lossless compression and everything is already pre-determined. Therefore my workflow is to paste into a graphics program, adjust the image and save as a suitable format before Inset > Image or drag and drop.
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If you want to save copied images in quick succession, say from a website, try right-clicking and and selecting Save image as… After defining the folder for the first image, it is quick adding new images to the same folder.
If you are getting a lot of screen images that you want to save in quick succession, you could try Greenshot, or I understand that you can set Windows PrtSc to save the images in a pre-defined folder.
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As this question has come up again, I thought I had better address this statement. Drag and drop in Windows is the same as Insert > Image; it copies the image file into LibreOffice, not the bitmap.
Copy and paste of images is normally best avoided but it is perfectly OK if the image is already optimised for a smaller file size in PNG such as Indexed colour, Greyscale, Black and white