No matter how far away you teleport after you set off one Shrieker, another cannot be set off. This means if you have an arrow or any projectile that belongs to a player constantly alerting a Shrieker in a force loaded chunk and Warden proof the immediate area, you can completely prevent Warden spawns. Demonstrated by ilmango's contraption. https://www.youtube.com/watch?v=Nmtbcw7miLg&t=492s

A potential solution is to make it so that if a player's sculk shrieker activated outside of a designated radius (say the radius where the player gets darkness from the shrieker block), ensure that the next time a sculk shrieker activates, make the game apply a cooldown that prevents another shrieker from activating if it's outside of that radius and only make shriekers within a radius activate. This fixes the issue while preserving warden farms (albeit nerfing them slightly but I don't think that's an issue).