IDLEX is an independently developed and distributed set of IDLE eXtensions.  We have nothing to do with it.

IDLE, as the name suggests and the doc spells out, is an Integrated  Development and Learning Environment.  It is not a production run environment.  For interactive development, one can close the shell window and reclaim its memory while keeping an editor window open.

16 million lines of screen output way outside of IDLE's intended use.  Why are you (mis)using it this way?

As you already discovered, an effectively infinite output stream can be sent to a console.  Command Prompt has a similar behavior.  If you want more saved, output to disk.

Or write your own gui for your simulations.  IDLE (and hence IDLEX) uses the tkinter wrapper of the tcl/tk GUI framework.  tcl/tk is also separately developed and distributed.  We just use it.  Its text widget does not come with any automatic size management.  But you could write your own insert wrapper that would delete a line for each line added after you deem the widget 'full'.

When I ran your sample with 64 bit 3.7.0b2 on Win10, the memory reported by Task Manager increased from 30 to 195 Mb or 165 MB net, much less than you report.  I once printed about 500,000 60 char lines.  I had either 12 or 24 GB memory at the time.

I am inclined to close this issue as 'third party' (IDLEX and tcl/tk) but I will let you respond first.