We use nitrogen in our race tyres when we did FIA and Brirish GT's. Normal air from a compressor has to high a water content and on a rear Porsche tyre we would see a 20psi increase with temperaratute which when you try and maintain an accuraccy of 0.5psi is a hell of a lot and can destroy the handling of a car. If nitrogen was not available we would use a diving compressor with a drier unit to get the air as dry as possible.
The other area we used nitrogen was in the dampers. With the high increase in temperature of a damper nitrogen would at least give us a smaller increase in pressure change.
As for road car tyres, not for me….