It may help to think of the cloud as a constantly changing and moving phenomenon. When an airplane flies through it, a hole isn't created. The consistency throughout the cloud with respect to visible moisture and reduced visibility is fairly constant at a given level. What this means for the observer is that as air swirls in the cloud, it draws more vapor...it fills in the "hole."
From the ground you see a cloud with rolls and tucks and edges and swirls; the cloud takes on a changing appearance with shadows...which hide the character of the cloud as you might see it up close.
At the cloud level wind blows, and the clouds appear to move with the wind. In reality, the wind blows through the clouds, which are constantly dissipating and forming...not just puffs of vapor blowing in the wind.
If you were able to sit next to the exit point in the cloud when the aircraft comes out of the cloud you would indeed see the cloud swirl in the wake of the exiting airplane, but that's hard to see from the ground.
I've flown formation with other aircraft in and out of clouds, above them, beneath them, and so forth, and the atmosphere is visibly disturbed by a passing aircraft...but being very far away makes it nearly impossible to see.
You may see this sometimes from the air, if you're riding in an aircraft and pass close to the contrail of anothe airplane, or see one pass by when you're near a cloud...you may get to see the cloud disturbance first hand.