What exactly does Rand need to read in there that he doesn't already know and sometimes know better?

That LTT's plan was reckless and he needs to think up something else? LTT told him his plan was flawed, that to seal off Shai'tan the way they did they had to touch him (the True Power) with the One Power and this is what lead to the counter-strike. SASG doesn't tell what went wrong, LTT did tell.

That linking with women is not the solution? Rand knows this too now. At the begininning of the book, because LTT just bitched against women refusing to help without explaining why, he thought this might be what went wrong and it lead to his outburst about Egwene. By the end of the book he should know better, after LTT told him why his plan was reckless. It doesn't take a genius to figure out why women refused to link for this...

That the CK was dangerous and reckless too? Rand knows this all too well and destroyed the AK. It doesn't matter that he doesn't know Latra Posae intended to seal off the whole area of SG, it would not have worked and Rand no longer has the possibility to do something like this.

The rest of the essay is "interesting", but interesting in the sense that Loial would enjoy reading it by the fireplace, not as source of important information Rand must know. The details about the WOS etc. he likely already knows from LTT.

It sounds very likely that after Dragonmount Rand will have "free" access to LTT's memories anyway, without any more interference from "the personality".

I seriously doubt RJ intended to use that essay in the series itself. It's like waiting for the scholar who wrote the Guide to show up to interview Faile Bashere about Perrin's Wolf Dream and so on. I don't think either the Guide or SASG (which is just an earlier version of the Sealing story from the Guide) will have any impact on the series.