1) If you're only using the generated column for filtering/sorting rows, you'd be better off using indexes on expressions? (https://www.postgresql.org/docs/current/indexes-expressional...)
2) Therefore, if you're instead interested in returning the generated columns' values, this feature would be useful in proportion to how expensive the expression you're using is, because you're saving time by precomputing the column rather than computing at query time.
Edit: I can also see the benefit of removing the burden on the person performing the query to have to remember the details of the expression, or in the server case, not having to duplicate the expression across code bases.