What you said is generally true, but it must be remembered the effort done 50 years ago by some Italian inventors about overcoming the limits posed by gas density by developing special regulators which can "assist" human breathing.No amount of training and equipment can overcome the physiological effects of breathing a gas that is too dense. Well, maybe some athletes have increased their ability to off-gas, I have no clue about that, but that's not the training we're talking about here.
Can it be done? Of course, people do it all the time, and have gone way past those limits. Will training minimize the risk? Of course. But there is a risk, and based on the research of Gavin Anthony and Simon Mitchell linked by @Imla, I consider this risk to be too high and completely unnecessary. So, I stand by my statement: I think diving below 40m on air is reckless.
At the time (1960-1970), "coral hunters" working in Sardinia, catching red coral trees for the jewelry industry, were considered the top-notch of scuba diving. These solo divers did routinely exceed 100 m depth in air, but, of course, the fatality rate was large.
One of them was Raimondo Bucher (already famous for other previous activities, such as the very first free diving depth records), who analysed the cause of several accidents and concluded that the major risk factor was CO2 poisoning, induced by the large WOB due to air density.
So he actively searched for a mitigation of this risk factor, developing the very first regulator operating "on offer" instead of "on demand".
Bucher patented his idea and attempted to license it to one of the major manufacturers of the time, Pirelli. But in the end the Bucher "offer" regulator never reached mass production, albeit several prototypes were built and tested with success.
More than 10 years later, another inventor, Luigi Ferraro, already known for the work he had done at Cressi (the Pinocchio Mask, the Rondine Fins, etc.), left the company and, with his friend Jacques Cousteau, founded his new company, called Technisub and based in Genoa.
Ferraro was well aware of the ideas of Bucher, but he preferred to develop his own "offer" regulator, called the Inject. This went in production and was commercialised worldwide, thanks to the affiliation of Technisub with La Spirotechnique by J. Cousteau, and hence with Aqualung.
These "offer" regulators had a big drawback, their "injecting" behaviour did cause a significant increase of air consumption. So, despite some commercial success, in the end the market went back to "demand" regulators.
This was definitely triggered by the success of the Scubapro Pilot, which, whilst remaining a "demand" regulator, thanks to its pilot valve, was minimising both inspiration and expiration effort even at great depth.
In conclusion, the idea that equipment cannot overcome the problems due to high density of air at large depth must be partially corrected: proper equipment can, at least partially, overcome these problems. However, this equipment in nowadays not anymore commercially available, and the drawbacks (air consumption, mechanical complexity) were not judged enough for keeping them in production.