Why did the Primarchs favour a Second Founding?

Why did the Primarchs favour a second founding?

The simple and honest answer is that it would prevent a mass civil war like the Horus Heresy from ever coming to fruition again. No one should command that many troops. And no primarch could then corrupt that many again. In that regard at least, the subsequent foundings have worked out rather well with only a few chapters turning traitor over the centuries. 

But let's have a quick look at some other motives.

Obviously Guilliman set the proverbial wheels in motion on this, and so was in favour of it. 

Corax is stated to have agreed with him and consented whole heartedly, despite rebuilding his legion in earnest in a certain, more dubious, manner. Perhaps he didn't want the limelight shone on the monstrous horde that he had built up and consented to prevent this coming to light.

Vulkan reportedly didn't like the Codex, but nonetheless, the low numbers of marines he had at the time meant that the Salamanders would not get a Second Founding chapter regardless. So it didn't matter presumably. 

Sanguinius was no longer around, so what else would the Blood Angels actually do anyway? Besides, they had to cope with all that Black Rage going around, so were hardly in a position to decline the order.

Ferrus Manus was similarly gone. The Iron Hands were shattered. They had presumably already had their own "Tempering" event wherein they independently agreed no one should command all the Iron Hands ever again. Thus setting them in lock step with Guilliman. 

Dorn was outraged. He really did not want to see the legions sundered. He was also in grief about the Emperor and blamed himself. Thus he set the stage for the Iron Cage incident. The survivors of that cleansing were rendered then in to chapters, having earned their forgiveness. 

Russ sided with Dorn and hated the idea. But then again, the Space Wolves are hardly the most codex-compliant chapter in existence in the first place anyway. Probably wouldn't make any difference!

Not much is known or written about what the Khan thought of it all. But it seems he agreed regardless. 

And as for The Lion. Well. Obviously he agreed. Better that than questions about you-know-who on you-know-where and searching for Fallen.