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Automatic indexing (idle question)
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I was envisioning SQLite keeping a set of statistics, like the ones prepared by <code>ANALYZE</code>.  In its simplest state, for each set of search/sort conditions (combinations of <code>WHERE</code> and <code>ORDER BY</code>), keep stats of how often it is used.  Every so often analyze this data to figure out which indexes would be most useful.  Then decide whether to make the changes right now or not.

Yes, there are a ton of considerations not included in the above, but that was my top-level understanding of how it would work.

And as stated upthread, making an index on each column is not a solution to any reasonable problem.  When I find databases where people have done this they usually betray other misunderstandings of SQL.