The Case-Shiller Index IS normalized for inflation.
"The indices kept by Standard and Poor are normalized to have a value of 100 in January 2000."
Source: https://en.wikipedia.org/wiki/Case%E2%80%93Shiller_index
"The indices kept by Standard and Poor are normalized to have a value of 100 in January 2000."
Source: https://en.wikipedia.org/wiki/Case%E2%80%93Shiller_index
This chart from the same wikipedia article seems to show that inflation adjusted (dotted line), the prices are less than 30% higher than in 2000: https://en.wikipedia.org/wiki/Case%E2%80%93Shiller_index#/me...