I don't really agree with the last bit (with the rest yes). This wasn't LTT, it was Rand's version of LTT, based seemingly on strongest, most traumatic memories (the last ones) and mixed with Rand's vision of who the Kinslayer was from the very dark, very twisted tales about him Rand knew of.

Rand rejected/repressed almost everything that contradicted that picture of LTT as a fairly dark madman. His subconscious knew better and a few things slipped through here and there, which Rand rejected. A specific example is when "LTT" told Rand he was much harder than he's ever been. Rand obviously had the memories to confirm that, but they were repressed.

We can even say Rand rejected most of LTT's personality. As LTT was a coping mechanism from the aspects of himself/his role Rand could not deal with, Rand's rejected virtually everything positive about the man (also what he feared too much, like mass destruction weaves... it's only in the last extreme of saving his life and those of his inner circle that Rand accessed those memories... and he couldn't cope with the truth it was him who could weave such destruction and he imagined that it was LTT taking over his body for that. It had positive sides too, this repression. For instance, his LTT memories feared the CK like the plague, and had Rand listened he would never have tried to heal saidin. He rejected those instinctive fears and so wasn't inhibited).

The Forsaken described LTT as soft-hearted (understand, "loving and caring" I guess), someone who didn't like to use people, who "stank of piety" (a strong defender of the Creator's design and the Pattern, then). All this didn't fit in Rand's vision of LTT, so Rand repressed those memories. Rand's version of LTT had nothing of the sociable/affable man, the beloved/admired leader, the man with a lot of experiences, bad and good, with dealing with people, and exercise of authority. Rand's construct of LTT was a terribly one-sided/twisted affair, a monster/madman/tyrant enamoured of honors that personally I find closer to what Ishamael/Demandred were truly like (Rand's vision of LTT seems to how a lot to memories of the Forsaken, in truth. That's how much Rand loathed the man that he tainted him with dark/evil sides). I don't think except between the counterstroke of the DO and his suicide the real LTT was ever this paranoid, obsessive, monster-like man. That's the construct Rand made out of a few memories and his own vision of the man, not the real Lews Therin. If you notice, every time a memory seeped that contradicted this picture, Rand tended to brush this aside as "raving madness". Eg: once in Tear Rand thought one more of his naive beliefs about economy, and a LTT memory surfaced to contradict this, and Rand thought this was all madness. It was very often like that, though some of it Rand just couldn't avoid and his LTT became more and more "layered"/complex as Rand went on (though he always remained "grey" at best, until DM in TGS when Rand remembered the whole man). There was a lot of valuable experience and even wisdom Rand could have tapped into, and that his subconcious tried to make emerge when he needed it, but Rand rejected all or at least most of it. That will probably all change now that the construct has been put away (it's not so dissimilar to Nynaeve's block, when you think of it). No more than Birgitte Rand will reject these experiences now. Rand coming back from DM will probably appear to have magically matured, spectacularly so. His beliefs about the world, the OP, leadership, relationships with his loved ones and his underlings, his respect for other people will likely have changed massively now that he doesn't repress the LTT memories. What used to be a big burden/threat to his sanity will now be a massive strength. Of course, LTT had no solution for the Last Battle, though Rand will have full knowledge and understanding of what didn't work, though.