No chance of that ever happening. All over Europe, most of the controllers would be fired if they ever did that. The radio would be very silent....
They probably could do it for FL100-FL200 GA though. One rarely sees another aircraft around up there.
One good reason they don't do this may be to maintain radio contact. Most non-commercial pilots, myself included, have no idea what the next frequency would be, and they keep changing around.
And if one goes non-radio, the 'lost comms' procedure comes in and you are implicitly cleared all the way to landing on the filed runway, and I don't think this idea goes down well with ATC.