So, I want to run this by everyone to see if I am repeating something that is generally understood.
Odium comes to Roshar. The goal is to Splinter Honor. Honor knows this. He lays a trap. The cost of possible Splintering (edit: of Honor) is that Odium must be bound to the Roshar system and therefore not be able to leave and chase other Shards. Something Honor would do - put himself between the danger and those it pursues.
The Oathpact suddenly makes sense. The way to keep Odium bound to a system is to have Odium Invest. How does one do it on Roshar? Give up its Investiture to create a lot of spren. The more spren, the higher one's Investment. So, Odium, by Oathpact, can battle Honor, but in the way that bounds him: by Investing in Roshar, and fighting the spren war.
Basically, the voidspren, the Unmade, *any other object* Invested by Odium on Roshar, makes Odium's Connection to Roshar higher. Which is why there MUST BE multiple Desolations - Odium must be permitted to grow its influence on Roshar to the point of active war. And this is why, short of Splintering Odium himself, this must repeat - if Odium's influence on Roshar wanes, he leaves the system and goes after other Shards. So, Honor chooses to play a long and dangerous game with Odium, just like Preservation chose with Ruin.
Also explains Hoid's "I sympathize with you, Dalinar, but what I seek to achieve and what you do are not one and the same, and *my* goals are more important!" Hoid wants Odium bound to Roshar. Odium whose influence is purged from Roshar is free to roam elsewhere. Hoid does not want it.
The problem right now is that Odium has splintered Honor. Achievement unlocked. Now is the time to leave the system (or Splinter Cultivation and leave the system). To do this, there must be an all-out war that ends with destruction of all Odium's assets on Roshar (at the cost of a massive devastation), and frees him.
TL;DR: Desolations and voidspren are the means of keeping Odium Connected to Roshar. Odium must be kept Invested.
This obviously skims over a lot of things (like, why Heralds). But overall, what am I missing?
Edit: It has been wisely pointed out that the Oathpact refers to the deal Honor made with the Heralds, not Odium. I struck that unfortunate phrase. The rest of the point remains salient: Honor promises Odium a chance to take him out, but Odium must Invest in Roshar to be able to Splinter Honor.