File's image well displays PNG icon not actual PNG
Copy paste the .png image onto the icon shown in the Inspector.


Open the .png with Preview
Select all with CMD+A
Copy with CMD+C
Select the application of which you want to change the icon.
Press CMD+I to open the Inspector
Click on the icon and paste the copied image using CMD+V


I have no clue why that works differently compared to dragging and dropping the image.