Of the SQL system database (master, model, msdb, tempdb) query store can only be used on msdb. I looked and don't find any documentation about query store on msdb.
While you can't see it in the GUI, it can be validated on your SQL 2016 instance
Validate Query Store is off
USE msdb
SELECT * FROM sys.database_query_store_options;
Turn Query Store on
USE [master]
GO
ALTER DATABASE msdb SET QUERY_STORE = ON
GO
ALTER DATABASE msdb SET QUERY_STORE (OPERATION_MODE = READ_WRITE
, INTERVAL_LENGTH_MINUTES = 30
, MAX_STORAGE_SIZE_MB = 1000
, QUERY_CAPTURE_MODE = AUTO)
GO
Validate Query Store is on
USE msdb
SELECT * FROM sys.database_query_store_options;
Of all the system database why is msdb the only one with the option to use Query Store, and what value does it add?
-- Stop Query Store
USE [master]
GO
ALTER DATABASE msdb SET QUERY_STORE = OFF
GO
Best Answer
Microsoft enabling a feature does not mean it will be useful for everyone. For systems using some of the features can mean relying on information stored in MSDB. In those cases Query Store can be useful.
Here are few articles about the usage and tuning of MSDB database objects.
msdb Database from books online.
MSDB Performance Tuning by Geoff N. Hiten
The Importance of Maintenance on MSDB by Tim Radney where he mentioned following:
I can see how query store can help in optimizing your indexing strategy and optimally querying/aggrgating/purging some of the information stored in MSDB.