The stonings would have been illegal under Roman law and would have resulted in severe punishment by the authorities. That’s exactly why in any case they would

The stonings would have been illegal under Roman law and would have resulted in severe punishment by the authorities. That’s exactly why in any case they would have had to obtain approval from/remand the case to Pilate. We have many other documented such incidents resulting in dire consequences. Pilate himself would have been averse to allow mob violence not just because it was illegal but because allowing such to take place as the Roman in charge would have likely merited punishment for him as well especially if it got more out of hand. Josephus is a great source on the historical situation of the time period, if you have the time to read the Antiquities and the Wars.