Why would an index fund with a fund company be better than buying the index itself?

for example. If I buy SPY, isn't that like buying an S&P 500 index fund? There are no management fees involved right?

Many funds allow you to trade with no transaction fee, the ETF will cost you a commission every time you buy or sell. If you want to make a one time purchase, an ETF makes sense. if you want to deposit a little bit of money periodically, the fund is the way to go.

And ETFs like SPY do charge management fees.

There are +s and -s to either. You need to weigh them.

+s for SPY are: you can buy and sell any time. Not just when the market closes.

-s for SPY are: brokerage commissions.

+s for mutual fund index offerings. No brokerage commissions. -s are that you can execute you transastion only after the market close.

Both have expenses. SPY averages 0.10%.

Note: Be aware that most of these are capitalization weighted. That is not my idea of having a diversified portfolio. There is one index fund based on the S&P 500 that is not capitalization weighted, maybe more, but only one that I know of. RSP. It has also outperformed SPY and performance is what matters.