The use of the "Master sensor for parent" precludes having a dependency on the ping (sensor) since the option to bind the sensor as the parent's dependency prevents setting a dependency on the sensor.

The same can be implemented on the parent device by selecting the child sensor as the dependency, thus freeing the ping up to be dependent on say, a DNS check.

The master sensor for parent, shouldn't be a toggle or prevent setting a dependency on the sensor, but should be a shortcut/script button, which when clicked, would set the dependency on the parent as the sensor which it's set as parent dependency button was pressed. If a different sensor's parent dependency button is pressed, there should be a dialog that the dependency on the parent is set and if they confirm the overwrite.
The sensor settings screen for dependency should not clear the parent's dependency, since that is also tied to schedule and reverting to inherit, instead of previous settings, is a blind change.
Currently the sensor/settings/Schedules, Dependencies, and Maintenance Window, Dependency Type / Master sensor for parent, is a blind, non-confirmed change to the parent. If the parent has a schedule, maintenance window or a set dependency using this function will update the settings without notice, warning or confirmation.

Additionally, if the master sensor for parent is selected, and then on the parent device, the dependency is changed, the sensor still shows that master sensor for parent is selected, but does not function.

The documentation needs to be a bit clearer on the side effects of using the feature