One thing is shooting (which if they want to, they can), and quite another is actually hitting the target. At the beginning of the war, it is true that the British and the Soviets learned to shoot whilst the tank was in motion. But both German and Soviet doctrines recommended stopping the tank, in order to hit the target. It makes sense to shoot in motion for suppression or area fire with high explosives.
There are many films with tanks shooting in motion, but they are usually propaganda or educational recordings. When it comes to images of real combats (where it is not so easy to calmly make a recording), tanks usually fire when they have stopped (as in the famous battle of the Cologne Cathedral between a Sherman, a Panther and a Pershing).
If I remember correctly, some Shermans, the M-36, the M-10 and the M-18, the Pershing (and I suppose some others) used gyro stabilizers, but they were neither manageable nor user friendly in combat conditions. Even today (and I speak in REAL combat conditions, not promotional videos) the Syrian army´s tanks – with some modern gyro stabilizers – usually stop to shoot, or do so moving at a very slow pace.