Why there are no open source games made with a popular engine?

The easiest option would be to make an example game and put it on the market place. There’s a few Unity projects like that as well.

A more complicated option would be to come up with some solution where someone could download the specific version of UE4 you used, and the developer have an automated process (an .exe?) that adds and appends the changes the developer made to the engine files, as well as contains the project files.