While I tried to spawn a warden with skulk shriekers, it won't spawn in all game modes.
There are reasons why it won't spawn a warden in an ancient city:

• It won't spawn a warden in all skulk shriekers and skulk sensors around the world.
• Even with survival mode, it won't spawn a warden either with skulk shriekers.
• It was discovered and used the ancient city days ago.
• I placed down 11 skulk shriekers and 2 lines of skulk sensors in skulk block or vein and it does nothing to spawn a warden with skulk shriekers.
• In a natural generated skulk shrieker in caves, it won't spawn a warden at a same reason.
• The light level to spawn a warden is very low.
• After I used one of these skulk shriekers, it does not have darkness effect included it.