Aren’t shut off valves located at the water meter like typically around here? …which, your flow through design picture indicates would shut off the sprinkler water with the domestic water.
The domestic and sprinkler shutoffs are separate. Those systems branch.
So if you have a clean water flow through sprinkler, then shutting the main won’t turn off water to the toilets.
Got another name for it “passive purge systems”. It avoids the need for backflow prevention to protect the public water system from stale sprinkler pipe water.
And, avoids the pressure drop of a backflow device.