disclaimer: i don't have a relevant technical reference handy, and i'm far from an expert on the area, which is vast, and i recognize you know things i don't about it. still, i do spend a lot of time reading papers with metallurgical micrographs in them†, and i think i figured out the answer to your question many years ago, so i will explain my understanding

except for the part about grain orientation, anyway

> In every rolling mill I've been in, there is a limited amount of reduction per pass through the mill, after which the metal needs to go for thermal treatment to be annealed to remove all the cold work. Every time you anneal the material, you completely resets the elongation (internal plastic strain) and strengthening due to work hardening. If they do too much reduction in one pass or at too low of a temperature, it cracks the material and makes it weaker.

as i understand it, this is exactly right, but you say it as if it's contradictory. strain hardening increases the yield strength of metal (by making it yield). it can also change the tensile strength, but to a much smaller degree. when the metal can no longer handle stress by yielding, in particular by yielding in a way that produces further work hardening, so that the yield is distributed over the metal rather than being concentrated wherever it starts, it cracks. that's why strain hardening metal makes it more prone to cracking. in general, a given metal is more prone to cracking when you harden it, whether you harden it by cold forging, case hardening, or quenching. (peening is the exception; it inhibits crack initiation by a different method.)

https://en.wikipedia.org/wiki/Work_hardening has an overview that talks about how this phenomenon can be either desirable or undesirable

the change in yield strength from cold working can be quite large, a factor of 4 or so. it doesn't change the ultimate tensile strength much (or at all in the case of your wire rope), but there are a lot of cases where what you care about is the yield strength, not the uts, because if the part yields by more than a tiny amount, it is out of tolerance and has therefore failed

(with respect to a36 steel, elongation at break, and wire rope, this is a minor detail, but it's possible to elongate it somewhat more through rolling than you can through wire-drawing. but you are certainly correct that you cannot elongate it 100×, and wire rope is mostly made by drawing, not by rolling.)

there are different kinds of heat treatment, but the most common kind for steel involves a phase transition to austenite and back, which does indeed destroy the entire grain structure of the steel, losing any potential advantage of forging, precisely as you say. i'd think this would also be mostly true for hot-forging, where steel is forged while still austenitic; the relevant grain structure for strength will be the one that the steel acquires when it leaves the austenite phase. there are other kinds of heat treatment (more commonly used with things like aluminum) that don't involve fully recrystallizing the metal, and i would expect some grain structure to survive those

probably none of that is telling you anything you don't already know, but perhaps it's a different way of thinking about the things you know that explains the apparent contradictions

as for which direction i would expect grain orientation to make things strongest in, i really have no idea at all

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† last night, for example, i read https://www.mdpi.com/2075-4701/8/2/91/pdf and https://www.jstage.jst.go.jp/article/jjspm/63/7/63_15-00089/..., but also parts of https://pure.tue.nl/ws/portalfiles/portal/1584410/617544.pdf, http://www.diva-portal.se/smash/get/diva2:1352113/FULLTEXT01..., https://yadda.icm.edu.pl/baztech/element/bwmeta1.element.baz..., https://www.imerys.com/public/2022-03/Specialty-Carbons-for-..., and https://backend.orbit.dtu.dk/ws/portalfiles/portal/200743982..., but i was maybe on a bit of an atypical metallurgy bender. none of these are more than marginally relevant to the questions at hand of forging, strain-hardening/work-hardening, and grain structure orientation