Over time, SPYs outperform most mutual funds when you add fees, etc. Seems like a no-brainer for long-term investing. What am I missing?

Well, for one thing, you're missing the fact that RSP has dramatically outperformed SPY over the last several years, consistently, and, they both track the same index. In addition, RZG has outperformed them both!
The difference between SPY and RSP is their construction: SPY is capitalization weighted while RSP is equal weighted. SPY is constructed so that the total capitalization of the index is computed and then each stock is added to SPY based on its share of that cap number. Thus, if you buy a SPY share, 40% of your holding will be in Apple. RSP on the other hand, has one share of all 500 stocks in the average in each share. For the last several years, equal weighted indices have been the best market performers. I added RZG to show you need more than one index in a portfolio and need to weight them accordingly in your holdings. At some point, the trick is to know when, the market preference for cap weight will overcome equal weight. Unless you (or your advisor) catch that switch, you will leave capital on the table.
Your belief that SPY is a "no-brainer"has merit to the degree that its costs may be lower than many mutual funds. But to scrimp on fees while under-performing the market doesn't seem like a very sound investment strategy to me.