Tom you invited friendly debate, so, respectfully, is a different view.
Thus a fast moving part with thin oil can support the same load as slow moving part with thicker oil.
The choice of oil Is far more complex than that. The loads on a small lathe, including medium sized lathes are very small compared to, say a car differential or transmission. Loads in the apron are seldom over one hundred pounds for the spur gears. For the size of the gears this is a tiny % of the maximum load.
The purpose of the oil is to both lubricate and remove contaminants from the gear. Thicker oils only do this well if they have sufficient radial velocity and oil exchange to do so. This is not the case in an apron gear set.
EP additives should be used for spur / hellical gears. (EP == extreme pressure).
Never us EP in the presence of brass no matter what the gear combination is.
Now as we do have bearings in the machine we must note that too low of a viscosity will cause the oil to escape the bearing too quickly thus small lathe == higher viscosity oil in the headstock. Faster speed also means lower viscosity. Roller bearings = 50% more viscosity.
This is a serious over-generalization, as many short pamphlets do. Bearings that are lubricated by oil can be oil bath, splash or flow lubricated. The viscosity in the headstock isn't solely for the bearings, or you would need dual lubrication in the headstock.
Oil in the headstock should be lighter then oil in the apron (unless it is some kind of older slow lathe) as headstock moves much faster. This way they can both support same load.
That is simply not how the apron works. You are right in saying the gears move slowly, but the speed of the gears has *nothing* to do with the required lubricity.
It is the combination of the temperature speed, pressure profile, and oil circulation characteristic that is crutial in choosing oils for anything. In my case, operating a lathe with 50wt oil in the apron at 7 deg C would be silly. it would not be within it's performance range. (that means that it is below it's critical temperature, and would provide significantly less lubrication than at 20 deg C). A few synthetic 50 wt oils can do this, but they probably have EP additives - catch-22.
SUMMARY
Any oil is better than none.
ISO 50 will work - for the service life in a hobby lathe - probably fine.
AW32 is recommended because of superior characteristics including lubricity, removal of contaminants, and oil circulation.
In no case will the pressure profile in the apron require heavy oil.
I'm going with what my vendor uses when he is paid thousands $ to rebuild machines. He uses AW32 in the apron of their 14 - 24" lathes - because of these superior characteristics, not because of some cost saving measure.