Compressed air contains many contaminants that impede tire performance. The deleterious effects of one of these contaminants, humidity (water vapor), can be understood through principles of gas chemistry.
When you fill up your tires with air from the atmosphere using an air compressor, you are also pumping liquid water and water vapor into your tires. Bleeding liquid water from the line doesn’t remove water vapor. Furthermore, if you don’t remove the liquid water, it builds up over time when you repeatedly pump air into your tires.
This is problematic for a number of reasons. First, when heated, the air in your tires can take up more of the moisture in your tires. In addition to diurnal temperature fluctuations, constant flexing of the tires over the course of driving for 30 minutes increases the temperature of the air in your tires by 10°C.
Suppose you inflate your tires at sea level, at 10°C (50°F). You then drive for a while during the day, and the outside air temperature increases to 30°C (86°F). The temperature of the air in your tires is now at 40°C (104°F). This increases the water-carrying capacity of the air in your tires by the following amount (https://www.engineeringtoolbox.com/maximum-moisture-content-air-d_1403.html):
It’s difficult to estimate the total impact of this additional water vapor on the pressure in your tires, because atmospheric humidity varies widely all over the world. Nevertheless, let’s assume that it only increases the pressure in your tires by 3 psi. This brings us to a second reason why the humidity from standard air compressors is problematic. According to the U.S. EPA, every psi drop in air pressure decreases your fuel economy by 4% (e.g., 22 mi/gal vs 25 mi/gal).
Compare a 25 mi/gal fuel economy to 22 mi/gal (as aforementioned), with a few reasonable assumptions:
You may be spending $100 more per year on fuel than you need to, and that’s assuming only minimal fluctuations in air pressure, minimal driving, and a relatively low cost of gasoline. A nitrogen tire inertion machine does not contain extraneous water, and thus avoids the fuel economy limitations inherent to standard compressed air.