Apparently at least Bluetooth has something called Current Time Service (CTS) (BLE GATT service 0x1805). If you pair a cheap "smartband" to a phone, it'll set itself, even without using any apps. Neat! I guess it uses CTS?
Nokia proposed using SIB9 5G time transmission as time syncing in clocks, the idea being that transmission is available openly even for non-subscriber. Softbank later proposed commercializing the service, which is unclear to me since surely the public transmission would be enough for casual users and anyone requiring more would already use full 5G to control the device anyway.
The issue is which time signature do you trust without selecting an SSID, maybe by power? But I agree this can be an issue albeit small one in my opinion