As far as I know, interception of civilian aircraft is done to assess a situation where the safe status of a flight is uncertain.
A Vueling A320 got intercepted some time ago when the French ATC weren't able to communicate with the pilot. The same airline some time later got another interception by the Dutch.
Intercepting the aircraft and watching the situation inside the cockpit and/or the cabin can help to assess whether there is a serious situation developing (and further actions can be taken, such as alerting emergency services on the ground, monitoring the flight path, continuing the interception procedure to try to improve the situation).
It's not about piloting the intercepted aircraft, but about assessing the status of the flight. I think it's just a matter of gaining some time if a hijacking occurs.