Why your application doesn't use a view? Or even better a table function?
Many places online recommend storing this collection of divided geometries as a materialized view, but I recently had to move it to a separate real table because inserting a single new record would take 15 minutes to update the view (on an RDS 4xlarge database). It could at least update concurrently, so other reads didn't block, but now that the the divided geometries are stored in a separate table I can add new records in under 5 seconds usually.