From a real scientist (my Ph.D. proves that) and racer (cages for lots of years)

Nitrogen does indeed have a lower mass than oxygen BUT oxygen does indeed penetrate rubbers better than nitrogen. There are two reasons racers use nitrogen (sometimes)- they are that it is dry and that a tank can be smaller and easier to haul/use (eg no electricity needed) than a compressor (in some sizes). Nitrogen filled tires hold pressure longer and have predictable pressure changes with temp. (Gases often penetrate materials in ways not so obvious to the untrained. For example, at low temps, carbon dioxide walks through many common plastics very rapidly but its slow enough at higher temps above liquid that soda in plastic bottles has a several month shelf life). Ordinary low pressure compressors make "wet" air (which is why they put drain valves on the tank) and while there are compressors that makes dry air, they either make it at very high pressure or are too large to be practically portable- and are expensive either way. The rate oxygen penetrates rubber is low enough to be of no importance at the track so any dry gas works about as well as a tank of nitrogen- eg a tank of compressed air gives the same result for short term use.

Liquid water makes gaseous water in proportion to temperature. Tires in race use will have carcass and tread temps that will usually be above or at the boiling point of water (note that the boiling point- the conversion temp) goes up a few degrees as pressure inside the tire increases (this difference is in fact the principle behind industrial steam sterilization times)- above boiling point converts all of the low volume of water drops that came in from the compressor to vapor and causes a step change in pressure. Race tires on cages start at much lower pressures than street tires (often below 20 psi) so the boiling point of water inside the tire is several degrees lower than for a street tire.
Street use tires will be below the boiling point of water but especially on hot pavement will get hot enough to vaporize some or all of the water depending on how much got in.

I don't consider the advantages of nitrogen to be worthwhile for street tires. Air is 80% nitrogen (approx) anyway, tires don't get as hot as when at the track, and I've got to check pressures fairly often anyway given the small volume of bike tires. Seasonal or other temp changes especially impact readings. When I have nitrogen or high pressure compressed air handy I'm happy to use it but I won't go out of my way (or pay $5) for it for street use.

The high temps of track use raise other sorts of issues not very relevant to street use- like flow of sealing washers that can create leaks, utility of various patch methods (most are dubious at best for race hot tires though I admit to using such when I had no other option) , heat cycle determination of tire life (race tires become effectively worthless long before they wear off the rubber surface and the balance of prime use time vs performance is often a deciding factor in races), etc etc.. Racing rubber in competition conditions is very different from street rubber to the extent that if you have only street tire experience, you haven't experienced anything very relevant to it.

Oh- I do ride a Honda (recently acquired Transalp) as well as a mess of BMWs ...