Assuming no entries or exits into a cap weighted index, there will be no trades. No trades mean no price pressure either way. So it would just be the active traders exerting price pressure. And index buyers and sellers would buy and sell everything which wouldn't misvalue any one stock.
I mean if everyone piled into the market, you would still get a bubble sure, but that would imply that at least some stocks were misvalued anyway, so we still aren't worse off.
'Intrinsic' value starts getting tricky very quickly. How do you go about defining it. You're implying it isn't the stock price, so assets minus liabilities? But then what about Uber, or Tesla.
What arbitrage opportunities are you making reference to? ETFs are basically valued via arbitrage, certain traders are allowed to swap the ETF for the basket of shares, or visa versa, so if the price moves away from the underlying shares, they arbitrage it away.