In the case of carbon steel, if the carbon content is approximately 0.76% (the eutectoid) it is the right combination for the BCC to transform into FCC at the lowest temperature (1335 degrees F).

The eutectic is the right combination of alloy content to produce the lowest melting temperature, but that's a different discussion.
The carbon content is high enough that rapid cooling results in a microstructure that is high strength, high hardness, but with low ductility and pretty poor toughness. We call the microstructure martensite. The martensite is BCC that is saturated with carbon, so the only way the carbon can be accommodated is to elongate to become body centered tetragonal (shaped like a shoe box). Tempering allows some of the excess carbon to come out of solution as carbides. Some hardness and strength are sacrificed to improve the toughness and ductility.

In the case where the eutectoid composition of iron and carbon is allowed to cool slowly, there is sufficient time for the excess carbon to come out of solution as layers of cementite. The resulting composite is BCC ferrite with very low carbon (around 0.005% carbon) and layers of cementite. Under magnification, it resembles Mother of Pearl, thus it is call Pearlite.

Referring to layer of cementite is an over simplification. That suggest stratification. It is more like the platelets of cementite intermixed with ferrite, but the intermixing is more ordered than random.

The key is the cementite. It is compound of iron and carbon; it is not an alloy. Without carbon, there is no pearlite.
Now ask yourself if aluminum is alloyed with carbon? The answer is no, thus no cementite and no pearlite.

The alloys added to aluminum can segregate under certain conditions. You mentioned the alloy of 6061 which is alloyed with silicon. If one attempts to weld 6061 without filler metal (autogenous), the silicon will form compounds that segregate along the grain boundaries and solidify at a lower temperature than the surrounding aluminum. One usually sees a spider web of cracks along the centerline of the weld along the grain boundaries.

If the welder deposit a fillet weld while using a filler metal like 4043, but attempts to advance the welding arc to ensure fusion to the root before adding filler metal, a recast structure will result in the root. It isn’t a good outcome.

Its the best description I can muster. I was up at 3:00 AM and it is now 11:55 PM. My brain is fried and I need to go to bed my friend. I hope my ramblings help.

Al