When I was a mechanic, we tried it on a race cars we prepared. Hm. Maybe two. The idea is to reduce unsprung weight as much as possible, and the second idea is that pure nitrogen is more stable than mixed compressed air. The results were indeed mixed. The driver said he could feel only a little difference, and even then he admitted it might have been his imagination. We saw slightly better wear patterns on the slicks, but again, that might have been the driver doing a better job. Be mindful that nitrogen works best on race tires which are engineered to be as light as possible. Street tires for any vehicle are significantly more robust and thus heavy in comparison. Reduction in unsprung weight is better achieved with attention to fasteners, brake components, and wheels. All of these can lead to decreased reliability, though.
Nitrogen in tires is the modern equivalent of fuel injection additives that used to fill parts shop shelves. Theory says yes, real-world application says no difference. If it makes you feel better about your tires, do it. I would keep my money and buy more gas for riding.