Indexed View ft. Count_Big - testing Index Substitution on Counts

indexviewtest.sql

IF (OBJECT_ID('Count_Test_View') IS NOT NULL)
    DROP VIEW Count_Test_View

IF (OBJECT_ID('Count_Test') IS NOT NULL)
    DROP TABLE Count_Test

CREATE TABLE Count_Test
(
    Id int Identity(1,1) PRIMARY KEY NOT NULL,
    value int
)
GO

CREATE VIEW Count_Test_View WITH SCHEMABINDING AS
(
    SELECT COUNT_BIG(*) as count
    FROM dbo.Count_Test
)
GO

CREATE UNIQUE CLUSTERED INDEX cuq ON Count_Test_View (count)
GO

-- Create some dummy data - takes approx 7 seconds for 1M rows
INSERT INTO Count_Test
  SELECT TOP 1000000 RAND()*1000
  FROM	(SELECT 1 as n FROM sys.messages m1 CROSS JOIN sys.messages AS m2) as t
  
-- none of the following seem to use the Indexed View to speed up the Count
SELECT COUNT(*) FROM Count_Test
SELECT COUNT(*) FROM Count_Test NOEXPAND
SELECT COUNT_BIG(*) FROM Count_Test
SELECT COUNT_BIG(*) FROM Count_Test NOEXPAND
SELECT * FROM Count_Test_View
SELECT * FROM Count_Test_View NOEXPAND