"Naive question - would the sort of forces and stresses experienced by the bearings in a bicycle frame really require specifically magic grease formulations?"
I'm no tribologist so I may be well wide of the mark but I'll try to answer! When selecting greases there are a number of considerations: speed, temperature, load carrying ability, protection against corrosion, miscibility etc. To address these considerations you can play with the choice of thickener, the base oil and various additives.
Choice of thickener - as cycling is a low speed application you don't want a grease that is too thick but similarly you don't want it to run right out od the bearing! For cycling you want to also consider how the thickener behaves at low temperatures (below zero) - you want it to still be able to leach out the lubricating oil! If the load is such that you need a thicker consistency this will affect its performance - to get around this there are load-enhancing additives that are £££ but entirely unnecessary for cycling - load is not really a limiting factor for us!
Base oil viscosity is usually selected based on speed and bearing size - for cycling I don't think we have anything that requires anything fancy.
Additives are of particular interest for us because with cycling you will get water ingress - so you want rust inhibiting additives. You also want an additive that stops the grease being washed out by water! This is why I recommended the trailer axle grease for marine applications! A lot of cycling greases also use friction-reducing additives such as Teflon.
The Italians I mentioned were probably trying to minimise friction as much as they could by using a grease that was not too thick but still matched the viscosity requirements. I guess the grease probably had special anti-friction, load-enhancing additives and silly temperature range (very low to very high!)
"Would an "average" bicycle-shaped-object notice if someone used some vaseline?
Initially probably not - I don't know what the lubrication properties of Vaseline are but I suspect that it is not a true grease - having a soap and oil. A grease is not what lubricates the bearing but rather the oil that is leeched out of the soap or thickener. With Vaseline I think we may be stuck purely with a very viscous lubricant - so high friction. Also I suspect it will react poorly to water ingress - therefore after a few weeks riding in a wet and salty Scottish winter the bearing would start to be affected by corrosion and potentially the Vaseline may be washed out by water!