The C43 is 4WD, with 30% of the drive sent to the front, according to the "bumpf" from Mercedes.
The problem seems to occur with other 4WD C Class cars, to a much lesser degree. The AMGs have unique front suspension geometry. The 2 WD C Class AMGs do not have this problem at all.
The Plus 8 doesn't have this problem, even though the engine power and tyre sizes are similar to the C43.
My conclusion: applying power to front wheels whilst on full lock make a minor problem a lot worse.
Comment: MB did a major software upgrade when they changed the tyres. Did this alter the torque to the front wheels on full lock at low speed?