Head rush moment: SQL may use information from histograms outside of the index it chooses for cardinality estimation.
Back to earth: If you just create a bunch of statistics instead of indexes, you’re (at best) using your Clustered Index for everything (which is still bad), or you’re using a HEAP for everything (which is usually worse). You’re still generally better off creating good indexes for your workload. They’ll get statistics objects created and associated with them, and if SQL thinks another column is interesting, it will create a single column statistics object for it, as long as you haven’t turned off auto create stats.
Sure, you can put on your black cloak and goat mask and create some multi-column or filtered statistics, but in the words of a wise man (Doug), you end up with more stats to maintain and understanding query behavior gets more difficult.
Erik argues that at the margin, keeping existing statistics up to date tends to be a better solution than creating new statistics.