I like this idea a lot. In a sense it's thinking of your application as a spreadsheet, where the database is a data tab and the frontend is the summary tabs. If there's a change to the data tab, the "spreadsheet engine" (or "materialized view engine" in your case) walks the dependency graph and updates all the relevant parts of the summary tabs.
In the Rollbar UI, we implemented a lot of this type of logic by hand to make our real-time aggregated Items list work (i.e. each time an Item has a new occurrence, we update its stats in the database and push the diff to connected clients). It would save an immense amount of code to have had a solution that did this out of the box.
The closest thing I'm aware of to this is BigQuery's materialized views ( https://cloud.google.com/bigquery/docs/materialized-views-in... ), which take care of making otherwise expensive queries cheap fast, but they are rather limited (i.e. no subqueries or joins), and don't have the "streaming output of changes" you describe.