By 'upper bound' here, I meant for the insured.

Above the deductible (and premium payments), the insured's exposure is largely lost time and headaches, the remaining financial burden is borne by the insurer. If anything, the presence of insurance might increase the amount of compensation an aggrieved party might be able to reap.

Agreed that there are plenty of places in the world where car-insurance is non-existent. In those places, accident victims may not receive proper compensation for their injuries/destroyed property or the recompense may not be monetary in nature.