If it's just stock-picking as opposed to getting access to a wider variety of investments, then it's very difficult for active stock picking to be worth anything. If stocks are owned just by stock-pickers and passive indexers, then they own the same stocks in the same proportion.
The only thing active funds can do is invest in things that passive indexes don't, or better take advantage of the "dumb money". Things like high-frequency trading definitely count here.
Pure stock-picking though? Yeah, anyone who outperforms is on the other side of trades that underperform, so you're going to run into issues.