We do not understand the timetable of the Lord. While he hears and answers prayers, He clearly does not do so according to our desires, but His own wisdom. For the Limhites, he did not immediately deliver them from bondage. However, things did improve for the Limhites.
What we have here is Mormon's assessment of the situation. Because Mormon understood God, he clearly gives God credit for the easing of the tensions and the burdens. A dispassionate historian might note that this is a relatively normal event. The further time took them from the conflicts, the lesser the immediate tensions. The longer they lived with the burdens, the more they were normal and less obviously imposed.
The faithful historian would note that God works with the world, and that both Mormon and the "dispassionate historian" were correct.