A lot of indices are something like "Top [N] stocks weighted by market cap in [industry/region/country]". You could call those stocks 'picked', but it's not as though someone is doing some deep analysis of the companies' fundamentals or trading history in order to decide which stocks make it into the index. I think that type of analysis is the kind of thing most people think of when they hear about 'stock picking'.

Yes, no index is perfect. But most of them provide more diversification than the average person would be able to achieve by manually managing a portfolio.