Claims of widespread famine have been exaggerated. Some of the letters used as evidence of famine are most likely reporting normal trade. Some of the earlier letters do not explain the destruction which occurred almost a century later, the famine would have to have been very long.
If the vast majority of the migrants were fleeing Anatolia because of famine, this does not explain the violent destruction in the region. Many of the cities which disappear in this period in the region have arrowheads in the walls and bodies in the streets and were evidentially destroyed by violent invasions. It is highly unlikely that fleeing migrants would have destroyed their own country.
Rumors of famine are vastly exaggerated and do not explain the violence across Anatolia and the Levant.