If possible, I would like to raise the priority of this issue.  I teach Python and I use IDLE every day.  This bug makes using IDLE for teaching extremely difficult.

Hopefully new information:

I have just bought a new Mac, which is running Catalina (MacOS 10.15).  I am using Python/IDLE 3.7.3, and I am seeing the same issue.  And it does seem to behave differently depending on if I created the file(s) on my computer (fails) vs downloading files from the internet (opens just fine). 

(For background info, I have used IDLE for years on my older Mac with MacOS 10.12 without seeing this problem.)

I have my Mac Finder set to open all ".py" files using IDLE.app in the Python 3.7 folder.

In the Finder, if I select one or more files and double click, each file opens in an editor window in IDLE.  But after that, with IDLE still open, double clicking on any other .py file is ignored.  I can edit and save any open file, but I can no longer open additional files by double clicking in the Finder, or by dragging a file to the IDLE icon in my Dock.

Further info:  If I am in IDLE and have an editing window open, then I choose to open a different file using File -> Open File, and navigate to another Python file, then the open file closes, and the new file opens - even if I have not saved any changed in the first file.

I never use the command line.  I just double click on Python files, and want to see them open in IDLE.  That's how I teach my students, and I typically have multiple small sample files open at the same time.  This bug makes it impossible to teach and work this way.

If it would help, I would be happy to create a small movie demonstrating this problem.