Although the concept of maintaining control and driveability is worthwhile, the idea of an impact system to initiate release of a spare inflated tube within the tire has its problems. The tire is the main contact of the car with the environment and a vehicle daily encounters many impacts on the road with bumps and litter on the road that might initiate inflation of the spare. There are tires now that can maintain vehicle stability for the temporary time to get to a service station based on the inner structure of the tire but I don't think they have been popular to date. Perhaps they are too expensive.

Perhaps an internal pressure sensitive actuator would be more useful to inflate an internal spare tube.

Another concept might be useful. Instead of one central tube, the tire could have many small sealed air pockets so the puncture of one pocket would not disable the tire. This would make impossible the change of inflation pressure with climate or terrain change but perhaps this is not over important.