I'm certainly not sold on the idea of having N2 in my tyres. Even when offered for free I don't bother. It's nigh on impossible for a tyre fitting shop to purge all the existing air from the tyre before filling unless they had very specialist equipment and in any case I'd have to invest in a bottle of N2 to keep topping up my tyres which I'm not going to be bothered with.It shouldn’t make any difference to pressure changes whether your tyres are filled with damp air or dry nitrogen. Boyles Law tells us that for any gas (or gas mixture) Pressure/(absolute) Temperature is constant if volume is constant. There may be arguments for using nitrogen but I don’t think they have anything to do with pressure. If there is liquid water in the tyre the argument would be different, but under any normal conditions the air in tyres should only contain water vapour - a gas.
The benefits are minimal unless you're an F1 team maybe.
Water vapour doesn't act as a gas in all situations. Vapour pressure increases with temperature, so water vapour in your tyres will produce an overall increase in pressure as they get hot. The only real benefit of N2 in tyres outside of top level motorsport is that it leaks less than O2 so should maintain the set pressure longer.