Thank you all, and I'm sorry for any misunderstanding that might have come about. =\
I don't think that it's solely the realisation that the Heralds broke their Pact that might have caused the Recreance, but the fact that finding out that the Heralds broke the pact that started to cause issues for the Knights Radiant themselves. We know that on Roshar ideas and thoughts are a powerful thing - hence why the spren exist. We also know that the Nahel Bond would not be able to survive through 'legal technicalities', so if a Knights Radiant had betrayed their oaths then the spren would start to die. I think that, after discovering that the Heralds broke the Oathpact they would no longer be able to follow the Heralds.
Do we know if Odium itself started to corrupt the Heralds due to how much time it had to spend with them between Desolations?
Edit:
Just a quick following up to my statement, and purely speculation, but what if Desolations are caused by the breaking of Oaths? We know that the Desolations only began once the Heralds 'broke' to the torture that they were subject to. This could be seen as a weakening of Honor by not being hono(u)rable - and thus weakening the thing that is binding Odium. It would also suggest that the Recreance led to the death of Honor himself, due to the sheer number of Oaths that were broken in one go.
If it can be shown that the First Ideal is not possible to be adhered to by the Knights Radiant, and it is inevitable that the Ideal will be broken, then it would also suggest that the existence of the Knights Radiant are partly a cause for the Desolations.