I think several databases actually do this.
For example, Alerting in MarkLogic
https://docs.marklogic.com/guide/search-dev/alerts#id_29203
Another example is
Percolations in Elastic Search
https://www.elastic.co/guide/en/elasticsearch/reference/curr...
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My personal view is that those are useful features, however, often they indicate poor architecture where developers did not create proper APIs that put data into the database, and instead rely on database 'triggers' (or percolations/alerts) to notify the 'world' about changes.
Those kinds of notifications, should really be coming from either data consumer or data producer APIs, -- not from the database engines.
https://www.postgresql.org/docs/9.0/sql-notify.html
Should be okay for 99% of needs no?
The idea of simply being able to listen to a query without any additional work sounds like it could be really attractive in certain situations.
Sounds a lot like RethinkDB changefeeds https://rethinkdb.com/docs/changefeeds/ maybe check that out first :^)
Of course, that is a testament to the quality of the documentation and the source code of PostgreSQL.
The fact that the Logical Decoding and Logical Output features were built for replication means that some decisions were taken not-in-favour of publishing changes, obviously, but it works pleasantly and straightforwardly. Even writing a custom logical output plugin would be simple, because Pg does all the transaction tracking, position tracking, change decoding etc.