When the Dow was first calculated, real time market capitalization for individual companies wasn't a thing. Prevailing market price was a decent enough proxy that Charles Dow could make an index of leading industrial firms out of prices (and price changes) alone.
As others have pointed out, over a long enough time period the Dow Jones has a high correlation with market cap weighted indices. Its annual volatility has been about 1.5 percentage points more a year, but average returns over any reasonable holding period are barely different than, say, the S&P 500.
There's an even better argument against the Dow than the price weighting though - the somewhat arbitrary company inclusions. One of the more interesting pieces of history is IBM's 40-year 'vacation' from the Dow. If IBM had stayed in for the 40 years after 1939 you could tack on another 5 figure number to today's index price.