...it "should" be replaced because such a fault could cause more problems.

I don't know it for a fact, but I wouldn't be surprised if a bad tire pressure sensor might cause a vehicle's computer to turn the engine off as soon it's put in gear. It's a safety thing. The computer's not going to let you drive off if it "thinks" the pressure in one of the tires is unsafe.

I recently retired my GMC van for a similar reason. Not a tire pressure sensor, but a bad anti-theft module. The vehicle doesn't even have an anti-theft package, but the computer still has the module in it. It's gone hinky and when it "thinks" someone is trying to steal the van, it shuts off the fuel injectors. Only a dealer can fix it, and the repair would probably cost more than a 12 year old van with 150K miles is worth.