Low tire pressure is a problem that causes reduced gas mileage (due to the greater rolling resistance of a soft tire) and increased tire wear (due to the greater heat buildup of a soft tire), and can contribute to accidents because of the uneven handling of a car with one soft tire.  Most people are vaguely aware of the fact that low tire pressure is bad, but they are not sure of the exact reasons and hence are not too concerned with checking their tires. 
Before the general introduction of radial tires, a soft bias-ply tire could be detected merely by looking at it.  Radial tires, because of their very flexible sidewalls, always look soft (compared to bias-ply tires); thus a radial tire whose pressure is low is very difficult to detect except by checking its pressure with a guage.  As a result, most people do not check the pressure in their tires until the tires are obviously quite soft; by this time, however, the tire has had its life reduced by several hundred miles.  In addition, a soft tire has degraded cornering and traction properties; it has been estimated that accidents due to low tire pressure cost 670 lives and $350 million annually while the fuel economy penalty has been estimated at $700 million annually. 
A loss of pressure that results in a soft, rather than a flat, tire is not caused by a puncture; it is the result of a slow leak, possibly past the bead of the tire where it contacts the rim.  A small pump that supplies a small quantity of air at the proper pressure to the tire would keep the tire at the proper pressure except if it got punctured.  There have been many such pumps proposed in the past, but all of them were too complex to be workable; furthermore, most of them had external connections to the vehicle's chassis.  This latter feature has two inherent drawbacks: (1) it makes it difficult, if not impossible, to use such a pump on the front wheels; (2) the external connections are subject to being accidentally or deliberately torn off.  A pump that is wholly inside the tire, however, does not have these drawbacks.