Famine hardly ended with the advent of agriculture.

If anything, farming made societies more susceptible to famine. Specialization of labor and dependence on a specific plot of land made it much harder to simply move somewhere else when food was scarce. Hunter-gatherers and herders were almost always nomadic and moved to wherever food was available.

Sure, but it isn't my claim.

Agriculture and farming were more stable/predictable source of food and shelter. Especially during winter.

Sure you can move, but nothing guarantees another tribe/predator isn't in the new place.