It's something the user should figure when and if they need to change a binding. It can be handled whilst on ground or on autopilot. Lack of control configuration can also be really inconvenient for hosts that wish to fly a different aircraft but do not have a profile even half set up (or fix a single binding on one aircraft), it would require disconnection of all clients.
The largest complaint I hear when introducing someone to DCS is that they need to quit out just to change a setting, "It's 2014!" they tell me. Setting up a profile before hand is the most obvious and logical decision but not everyone is willing or at times even understanding of what to bind.
In the end, it is a feature of convenience more than necessity. Those of us who have played for a while may not be so worried by such a thing, though I certainly view pausing as a non-issue.