Looks like it’s a feature: https://support.apple.com/en-us/105120

To save a click:

* Lockdown Mode needs to be turned on separately for your iPhone, iPad, and Mac.

* When you turn on Lockdown Mode for your iPhone, it's automatically turned on for your paired Apple Watch.

* When you turn on Lockdown Mode for one of your devices, you get prompts to turn it on for your other supported Apple devices.