The prophecies all suggest very strongly this just couldn't be done, either because the Wheel couldn't see a way, or because the Wheel calculated this wasn't a winning way to go. To become the true champion of life and of the Light he now is, Rand had to go through near absolute darkness, even touch Shai'tan to really understand what he faced. Before he could defeat Shai'tan, Rand had to reach bottom and decide to stand for life and salvation, with all this encompasses... love and compassion, acceptance of loss, acceptance of death.

In much the same way, the world was not ready for what is about to happen at the Fields of Merrilor. Rand had to become the lord of chaos, and break the chains of the "old order", which had too much self-interests, and was way too much penetrated by the Shadow. To make the apples falls, Rand had to shake the tree really, really hard. Then he would be able to see which are rotten, or full of hidden worms, and which can go in the basket.

It took the Tower Coup for AS to even begin to contemplate the truth of the Black Ajah, and it's in the midst of chaos they could be dealt with. By and large, it's in chaos everything happened... the Aiel accepted to change because their beliefs were shaken to the core, and their society almost fell apart.

The Shadow was taking massive advantage of Order... controlling through the power/authority of those in place, exacerbating hatred/prejudices/frustration/fears, fuelling ambitions. By bringing it all down, Rand and his inner circle (and after him, the character who's had the largest chaotic impact is Egwene.. but they all played a part, including Tuon) gradually made the Shadow lose a lot of its control on the world, and also brought the people and nations to the brink of despair, to the point the world at large has an epiphany and each one makes the choice to stand for life and salvation or not. Rand is now going to guide the world toward that choice, soon.

In a perfect world, Rand would have accepted LTT and gain wisdom and authority very early, then secure the collaboration of the WT, envision with the AS the Cleansing of saidin before he even proposed to seek male channellers etc. He would have made use of LTT's charisma and experience to become a beloved and respected figure, not a political or war leader, but a guide. He would have ignored those who refused to join his alliance at first, sooner or later they would come or their people who abandon them. Of course, none of that stood ANY chance of ever working. It couldn't be done without the WT support - and indeed Siuan and Moiraine hoped to do just that - but the truth was the WT had nowhere near the prestige and moral authority it would have needed to bring the world behind Rand. It would have met opposition from all sides, and the Shadow had darkened the Legend of LTT to make him the most feared and reviled man alive, so the world would never have "accepted" LTT. It's a measure of its desperation and fear that the world doesn't freak out about this at this point (to an extent, Egwene and the WT still do freak out a bit...).

Of course, there's absolutely no way the entrenched and hidden forces of the Shadow would have let such an alliance of the Light emerge peacefully and in good order either, and if against all odds it started happening, and Rand had gained the sort of powers to oppose Shai'tan he's gained after DM too early, Shai'tan would have immediately seen the peril and precipitated the world into a new War of Shadow before it was ready to face it. The Wheel has rather made Rand throw the world in chaos, fooling the Shadow into thinking Rand had become an asset and was doing the DO's job for him.... The Shadow has not realized in time that as the world fell in chaos, its grasp on the people/factions/nations was also falling apart.. leaving at the end a Seanchan empire free of the Forsaken, a WT cleansed of DF, a reborn Children of the Light order, and so on and so on - even purging all the "fanatics of the Light" that threatened to lead the world to another SL (Masema, Asunawa etc.).

It's perfectly all right for Rand to blame himself and to wish he's done things differently (Egwene has similar regrets/blames) -it's a proof of how far he's come that he can see this now, and he has made many terrible choices and costly mistakes (the BT may become his most bloody mistake), and his hands are covered in blood. The things is, he couldn't do things much differently, really - it's part of the price he has pay that he must go through this, but it's perfectly sane of Rand to regret this, feel pain for this and wish he could have done things differently as only a man like this, conscious of everything that has gone wrong, could come to understand how he must lead the Light as a Guide and not with the tyranny with which Moridin leads the Shadow, and what sort of champion he must be to stand a chance to win, he needed to make all those mistakes, and even more importantly to come to realize before it's too late that it was the wrong way to fight the Shadow. Before he could oppose Shai'tan, Rand needed to fight the darkness in humanity, and win.

The massive gamble of the Wheel was that it could let the Dragon go so deep into darkness so he could choose to fully embrace the Light. I suspect this is the real strength of the Dragon's soul that he could achieve all this: go almost to the brink of destroying the world and come back on his own, touch Shai'tan and see first hand what it made possible (save his life, and Min's, free himself... but risking enslavement to the DO...) and even after that decide of his on free will to reject Shai'tan and power, and become the man who came down the mountain.