I think the concept of using nitrogen isn't about choosing an ideal gas, but more about eliminating water vapor in the air.

Water condensing and evaporating doesn't expand/contract as predictably as any gas, and is the main cause of concern for racing tires where the temperatures are regularly over 100 degress C, (212F if you're a nascar fan).

Oxygen breaks stuff down quickly, and nitrogen is abundant and cheap. So use pure nitrogen not because it's pure, but because it's dry.

I'm probably totally wrong, so no need to bite my head off if I am, but that's my 2cents.