In the video here of an airshow take-off, it's noticeable that when the brakes are released there's a brief but pronounced fluctuation in pitch as the aircraft accelerates.
This is something you see in very fast accelerating cars / dragsters, but I believe that is caused by the torque through the rear wheels, which is obviously not the cause here.
The same thing can be seen on an F-16 but much less pronounced.
Certainly for the Typhoon, the nose-wheel oleo doesn't seem to be particularly compressed as it's held under braking. I'd guess that you want to ensure that there's no chance even the slightest bit of any upward vector in the engine thrust while you sit on the tarmac, otherwise your brakes might not work, but that doesn't really explain the wobbling.