There is no real benefit for street use. On my previous car, which i use to track regularly, i did the experiment and tried nitrogen.
With air in the tyres, under heavy load and during the course of a 20 minute session on track, it was not uncommon for tyre pressures to increase beyond 12PSI. With Nitrogen in the tyres, pressure never changed by more than 2PSI. This allowed me to run my preferred pressure all of the time - street or track - without having to reduce pressure on track to ensure i achieve optimum grip during a session. The added benefit of the nitrogen, pressure wise, was that my tyre pressure were right from the very start meaning more consistent lap times throughout a 20 minute session.
Between two sets of tyres, both identical size, type and brand on the same car, one was fitted with Nitrogen and the other not. The set without the nitrogen provided around 7500km less life. This was with an equal share of track work on the same tracks. I might also add that my driving style changed for the better during that period - so it may be a coincidence that the nitrogen filled tyres provided greater life.
I have no doubt that the nitrogen was a massive improvement in pressure stability for track use. For road use, i wouldn't bother - it made no difference, in my experience.
As for the cost - BJT use to charge $5 per tyre AND provide free refills/topups for the life of the tyres. Hardly and extrodinary money making excercise...