You forget dividends. If the correlation among stocks is too close to 1, it means that stock prices do not adequately reflect earnings and dividends. So the incentive not to buy index funds would grow and that would make correlations stop growing.
Also, the S&P 500 is a market cap based index, which means that passive investors have to ape active investors. So even a small minority of active investors would dominate price formation.
Ultimately, I think, the impact of ETFs on correlations will be limited.
Dividends are included in the returns when computing correlations. Hedge funds make bets on stocks over performing or under performing compared to a benchmark. If all stocks perform the same, there is no hedge because the weight of a stock in the portfolio does not impact portfolio return.
Also, the S&P 500 is a market cap based index, which means that passive investors have to ape active investors. So even a small minority of active investors would dominate price formation.
Ultimately, I think, the impact of ETFs on correlations will be limited.