Engine friction model

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I've run the simulation with engine friction torque disabled(-1NM). This helped to get a more precise idea of the issue. It is caused by locked up rear wheels, or to be more precise the transition from locked to rolling wheels. Engine friction enhances the effect by increasing the load transition on the driven wheels.

Immediately after releasing the brakes we have rear wheels still at full slip and 0 RPM accelerated by the engine. One of the wheels will get more grip than the other at some moment (due to load, contact velocity, engine torque, rear left wheel for left hand drive cars for example) and initiate oversteer as the overall grip is still very low. This is the point where TCS helps by braking this wheel, almost acting like stability control. ABS helps to prevent to get there in the first place by avoiding wheel lock.

I think one could try to add some auto clutch traction control functionality to make cars more controllable without ABS/TCS, keep clutch open on overrun if the wheels are beyond the ideal slip value. The TCS/ABS is more effective here though by acting directly on the affected wheel.