Are you sure you did the math right on casting recipes? Did you forget about the innate 50% productivity foundries and EM plants get?

Eh - it's pretty close for normal tier T3 productivity - e.g. Engines:

Pipe Casting - 5MI -> 1.5 pipes (3.33 MI/Pipe) (Casting iron at +90% productivity and then assembling pipe is worse - 5.2MI/pipe)
Steel Casting - 25MI -> 1.9 Steel (13.15 MI/Steel)
Gear Casting - 10MI -> 1.9 Gears (5.26 MI/Gear)

Engine Unit Casting - 35 MI -> 1.9 Engines (18.42 MI/Engine)
Engine Unit Assembling - 2 pipe/1 steel/1 gear -> (6.66 + 13.15 + 5.26 = ) 25.07 MI -> 1.4 engines (17.9 MI/Engine)

Once you start bringing quality productivity modules and Steel productivity research into it then it tips further to Assembling - as the longer production chain benefits more, and the cost of steel goes way down

Pipe Casting - unchanged (iron plates -> pipe is still not there, 4MI/pipe)
Steel Casting - 25MI -> 4 Steel (6.25 MI/Steel)
Gear Casting - 10MI -> 2.5 Gears (4 MI/Gear)

Engine Unit Casting - 35MI -> 2.5 Engines (14 MI/Engine)
Engine Unit Assembling - 2 pipe/1 steel/1 gear -> (6.66 + 6.25 + 4 = ) 16.91 MI -> 2 engines (8.45 MI/Engine)

All of the math that I did do ignores quality entirely because I thought that was a bit too much of a cheapening of recipes to account for it, I also accounted for not just innate productivity but also using as many productivity modules as possible when calculating the cost of the normal way to get things, and when setting the cost for the casting version I tried to account for innate productivity of the foundry as to not make things really silly (not accounting for it resulted in red bullets costing as much iron as yellow bullets with the math I used)

I also did not account for the productivity researches as I think they are actively a bad addition that shouldn't have been added and will never not play with my mod that outright disables them.

Wow, I guess I genuinely did mess up the math here and there, I'll look into doing a bit of adjusting.

Modules shouldn't be counted because the foundry has the same number of slots for those anyway. But melting ore adds a +50% productivity bonus itself, which messes with those ratios as well. Overall, the foundry IS the best choice for every recipe in its list because the ingredients and product rates are balanced accounting for all these things. Easiest way to test is to put 100 ore through a given chain of production buildings and seeing what it ends up producing. Turns out, the foundry wins. Even with copper cable, surprisingly.

Modules shouldn't be counted because the foundry has the same number of slots for those anyway. But melting ore adds a +50% productivity bonus itself, which messes with those ratios as well. Overall, the foundry IS the best choice for every recipe in its list because the ingredients and product rates are balanced accounting for all these things. Easiest way to test is to put 100 ore through a given chain of production buildings and seeing what it ends up producing. Turns out, the foundry wins. Even with copper cable, surprisingly.

The comparison is not with Ore -> Iron Plates (Furnace) -> Gear/Pipe/Steel -> Engine, it's with Ore -> Molten Iron -> Iron Plate (Foundry) -> Gear/Pipe/Steel (though some of these are more efficient to cast directly depending on quality tier of productivity modules) -> Engine. You still get the base foundry bonus, but additional processing steps give more chances for productivity to kick in.

Even your copper cable example suffers from this at higher productivity.

Foundry: 5 Molten Copper -> 3 Copper Cable (5 with max modules) = 1.33(1) Molten Copper per Cable

Foundry: 20 Molten Copper -> 3 Copper Plates (5 with max modules ) = 6.66(4) Molten Copper per Plate
EM Plant: 1 Copper Plate -> 3 Copper Cable (5.5 with max modules) = 2.22(0.73) Molten Copper per Plate

At Legendary T3 Productivity, you use over 25% less copper per cable by casting and processing it in the EM plant

Not sure how you ended up with less copper per wire with the EM plant setup, all the math and practical tests I've done have shown that (which have admittedly only been for the single ingredient chains) Have shown that just a foundry with legendary productivity 3s is equal or better than the multi step processing.

Then you did both wrong - EM plants being more efficient has been well documented (e.g. https://old.reddit.com/r/factorio/comments/1jzf284/what_is_better_em_plants_making_wires_from_copper/mn5uwj5/)

Oh, you're talking in vanilla? I thought you meant with my mod enabled.