This used to work fine - I did it all the time over at https://discourse.camra.org.uk - snipping screen images using Winsnap (or Snipper) and pasting into Edge. Stopped working when we upgraded to “Discourse 1.9.0.beta15” which is the same version as is being run here. Paste into composer doesn’t work here either.
Reproduced on both the most recent Fall Creators edition and older Creators edition. Microsoft Edge 40.15063.674.0 and Microsoft EdgeHTML 15.15063
Works fine with Chrome.