Generally you want the statistics to be automatically created and maintained.
There are exceptions – if your database is routinely updated by a high-volume batch update, you might want to disable statistics during the update and then turn them on after the update completes.
Otherwise, maintaining the statistics helps the query optimizer to properly execute the queries. This is true for all database engines.
If your statistics get “stale” the query optimizer may execute queries in a non-optimal manner, possibly leading to table scans and other performance-killing strategies.