The main benefit was that cast-iron could be made before steel was invented, it does not retain heat better than aluminum alloys. Cast-iron pans heat less evenly and must be made thicker than their aluminum counterparts.
Many stainless pans will have cast-iron handles because it conducts heat worse than steel or aluminum, and will not get hot to the touch as quickly.
You're missing the forest for the trees. Cast iron pans retain heat better than aluminum pans because cast iron pans are 4mm thick and aluminum pans aren't 6mm thick.
(Also it does retain heat better. [EDIT: by thickness, not by weight. The comment below is also correct.])
https://www.centurylife.org/heat-retention-myths-and-facts-d...
https://www.makeitfrom.com/compare/6061-AlMg1SiCu-3.3214-H20...
For most day-to-day cooking where you're ingredients are in direct contact with the pan over a burner (sautés, searing etc) heat retention can actually be bad (it's difficult to adjust the temperature). For specific tasks, cast iron excels, that's why you don't see a lot of copper deep fryers.
(This is mentioned in the 2 experiments that person runs in their kitchen that you posted)
In the end, it didnt cook that much better than my All-Clad D7. So I just stayed with that. But I have never cooked with anything so brimming with heat and ready to pour it into absolutely anything that came into contact with it.
Actually, both "steels" and "cast iron" are iron-carbon alloys, and we have evidence of quench hardened carbon-alloy "steels" thousands of years before the first cast iron pieces.
While we tend to think of bronze age as not featuring iron, the truth is that steel production dates back almost 4,000 years.
While cast iron cookware predates other steel cookwares, it's likely because it was far cheaper and easier to cast cast-iron into pot or pan shapes than it was to work mega-hot steels, which was reserved for much more expensive and important uses.
We started getting cast iron once we could get the temperature up to melting, then the optimized steels once we figured out how to add oxygen to the cast iron and burn out the excess carbon.
It's still possible to get higher carbon content out of a bloomery to get steel, but highly unlikely... And you'd get what, a nail's worth from 3 people's labour over a couple of days? {Mine the ore/grab it from a swamp, bake it, make charcoal, make the bloomery, run the bloomery, consolidate the bloom}
https://www.engineeringtoolbox.com/specific-heat-metals-d_15... says that aluminum has twice the specific heat capacity of cast iron, and another page on that site says that it has about four times the thermal conductivity. So if your goal is to dump as much heat into your food as fast as possible, aluminum is definitely the way to go. But if you want slower heating, iron may be better.
With specific heats of 0.91 kcal/(kg⋅K) for aluminium and 0.46 kcal/(kg⋅K) for cast iron, this works out to
Aluminium: ~2500 kcal/(kg⋅m³)
Cast iron: ~3100 - 3600 kcal/(kg⋅m³)
So for a pan of the same thickness/shape, cast iron should have a heat capacity that's 25-45% higher.
I don't know if such thick aluminium pans are available, though.