How to drop files from Desktop to Finder windows in a sane way?
There are multiple ways to achieve it. 

Using hot corners


Slide Your mouse to the hot corner to show Desktop
Drag Your file (do not drop)
Slide once again to hot corner
Drop the file to the app 


Using keyboard shortcuts


Show Desktop with ⌃ CTRL+↓ Down arrow
Drag the file (You may need to click on Desktop first to activate Finder)
Then ⌘ CMD+⇥ TAB to previous app and drop it


Using the trackpad


Show Desktop with gesture (spread four fingers on trackpad)
Drag the file
Slide on top of the app icon on Dock
Slide on top of the window You want
Drop the file