This may make sense in theory but in reality is wrong. The DJIA has historically had a very close correlation to the S&P. Plus there is an inescapable psychological aspect to the Dow that is unique. When the Dow is off 1500 points it hits much differently than the S&P falling 200 points.
I have a feeling that is because every company in the DJIA is also in S&P, and most are very heavily weighted in S&P. Rather then companies within the DJIA doing as good as companies in the S&P.