Nitrogen molecules are larger than straight air. Thus they take longer to pass through the tire, so you don't have to inflate as often on long hauls. For the track pointless.
I run water+water wetter in my tires in the summer. Drain it and switch to coolant in the winter.
When you compress air, the first thing to drop from it is water vapour. So I agree with Brian, most of the moisture is from applying the beadAir is 78% nitrogen and 20% oxygen. So only 20% is "smaller" if it leaks out then after the next fill-up of air you would have 93% nitrogen, next time almost 99% nitrogen....
As noted above the real reason is water content. Put a dryer on your compressor if you are that worried about it.