> How big is the range on one of these?
As always with RF propagation, it depends. They're frequently in the 315Mhz band, so should be roughly similar to garage door openers, remote controls, etc.
> Random sensors around it that aren't already paired to their own car.
There's no handshake -- TPMS sensors are generally unencrypted broadcast devices. A car will see a lot of sensors. (and you can set up an antenna and track cars driving down your street) The "pairing" is simply the vehicle remembering which ones is theirs.
> Also it could wait for you to complete an entire trip or two.
It could. Now add the complication of: spare tires. And also, some but not all vehicles store the positionality of the sensor, so they can tell you which tire is low.
But if you're going to give the system so much hysteresis, you might as well just save the money and use the ABS-sensor based system that other vehicles use. These don't require any additional sensors or programming, but they are slower to react and don't provide pressure readings. The reason automakers use direct sensor systems is to provide a more direct and immediate reading.
> "Safety" in the sense that the little warning light usually gets you to do something about it eventually? Is this data going into anything where the correctness is a big deal?
It is a big enough deal that the reason many cars have them is to comply with the legal requirement that they have them. Before the light (and better cars have textual warnings), you'd have to manually check your tire pressure to identify an underinflated tire, leading to many people driving on them for extended periods of time and experiencing rapid unscheduled failures.