Why does "airplane mode" turn off Bluetooth and WLAN if I can just turn them on again?
"Airplane mode" is a convenience feature provided by the phone manufacturer. You can choose to turn it off anytime in violation of the rules, so there is no difference there. 

What it does may not match the regulation in any particular geography as rules vary. Regardless of any particular device the airline sets rules to ensure that no device: 

1) Interferes with navigation signals required by the aircraft, particularly at landing

2) Confuses cellphone towers on the ground which expect radio signals in roughly a planar orientation near the ground

The airline gets its rules from the FAA/EASA... and indirectly from the FCC... What was considered "airplane mode" by the FAA changed in 2013. Testing determined that wifi and bluetooth did not cause sufficient interference with ground based nav signals, so that prohibition was relaxed. An old phone's "airplane mode" may be too restrictive.

There was no change to the rule on cellphone voice communication, which remained prohibited. Once the aircraft is sufficiently high no ground based cell tower can receive any signal, so this prohibition mid-flight is effectively meaningless.