Rather than request a specific solution, I'll state what new problems need to be solved.

For teaching purposes in live demos, it is essential to have a clear visual distinction between the inputs and outputs:

    >>> beatles = ['john', 'paul', 'ringo', 'george']
    >>> [name.capitalize() for name in beatles]
    ['John', 'Paul', 'Ringo', 'George']
    >>> [name for name in beatles if 'n' in name]
    ['john', 'ringo']

This doesn't work nearly as well:

    beatles = ['john', 'paul', 'ringo', 'george']
    [name.capitalize() for name in beatles]
    ['John', 'Paul', 'Ringo', 'George']
    [name for name in beatles if 'n' in name]
    ['john', 'ringo']

With the sidebar, the ps1 prompt helps a little, but gray separator bar visually runs the input and output text together and even causes consecutive inputs to visually be merged.  The strongest separator, the unindent, has been lost.

    >>>|beatles = ['john', 'paul', 'ringo', 'george']
       |[name.capitalize() for name in beatles]
    >>>|['John', 'Paul', 'Ringo', 'George']
       |[name for name in beatles if 'n' in name]
    >>>|['john', 'ringo']

I believe that if you consult a trained graphic designer (i.e. one who can name the 7 elements of graphic design and describe how they are used), they will confirm that the new display is problematic.  To make data groups (inputs and outputs) visually distinct, we can change alignment, change vertical spacing, remove strong vertical lines, change color, etc.).  But if you align the text and run a vertical line separating it from the PS1 prompt, then the distinction is blurred.  At least this is what I was taught in graphic design courses.  

Almost the entire purpose of graphic design in an IDE is to help the eye either group together like pieces of information or to help the eye create distinctions between dissimilar things.  We give elements the same color if they are related and different colors if unrelated.  We bring like information together by placing it close together or by giving it the same alignment.  We push things apart and disconnect them by drawing a separator line (in the case at hand, the ps1 prompts are clipped-off in a separate window from the text they were intended to annotate).

If we have to keep the sidebar, some vertical separation would help (as it does in ipython):

    >>>|beatles = ['john', 'paul', 'ringo', 'george']
       |[name.capitalize() for name in beatles]
       | 
    >>>|['John', 'Paul', 'Ringo', 'George']
       |[name for name in beatles if 'n' in name]
       |
    >>>|['john', 'ringo']
       |

This added spacing would help separate consecutive statements but would cost eating up valuable vertical space and would not help with visually distinguishing the input from the output.

You could take out the vertical line and get an improvement:

    >>> beatles = ['john', 'paul', 'ringo', 'george']
        [name.capitalize() for name in beatles]
       
    >>> ['John', 'Paul', 'Ringo', 'George']
        [name for name in beatles if 'n' in name]
       
    >>> ['john', 'ringo']

This is better, but could be improved by unindenting to distinguish the inputs and outputs, which just about takes us back to where we started from (not just in IDLE, but what you see in books, presentations, and blog posts):
       
    >>> beatles = ['john', 'paul', 'ringo', 'george']

    >>> [name.capitalize() for name in beatles]
    ['John', 'Paul', 'Ringo', 'George']

    >>> [name for name in beatles if 'n' in name]
    ['john', 'ringo']

Another desirable feature is the ability to cut and paste snippets into docstrings.  This is essential not just for doctest, but even for untested examples in docstrings.
Those examples, need to be recognizable to humans as interactive sessions with outputs clearly distinguished from inputs.  When I tried out the new sidebar in prep for a class, it was impossible to include the ps1 prompts in a cut and paste selection.  They had to be manually typed back in.  

Lastly, for live demos in presentations, it is desirable to have a clear screen, free of distracting artifacts.  The sidebar is such an artifact -- you would never see such a thing in a book or slide presentation.  Also, for live demos, large fonts are necessary which means that screen space is at a premium and the loss of horizontal space matters.