why are some index funds closed to new investors, for example, this one: VGHCX (https://flagship.vanguard.com/VGApp/hnw/FundsSnapshot?FundId=0052&FundIntExt=INT) ?

20% annualized return since 1984? sounds like they realize that people pay big bucks in management fees to get into hedge funds that earn half that.

why are some index funds closed to new investors, for example, this one: VGHCX (https://flagship.vanguard.com/VGApp/hnw/FundsSnapshot?FundId=0052&FundIntExt=INT) ?

This one's easy. It isn't an index fund. It is an actively managed sector fund. Like with any actively managed fund, it becomes less nimble as its assets become bloated. It is very difficult for a bloated fund to outperform the market, which is the goal of any index fund.