The drought explanation seems particularly plausible for the Hittites, IMO. They had grain storage, but ~3 years of drought would exhaust that. So if the climate becomes just a bit drier the chance of such a three year run increases enough to likely crash their society.
Today we have a huge buffer from the large use of grain to feed animals. In a crisis it could be diverted as human food, with some effort. Large geographic range from global shipping also smooths out blips. Still, a Toba-like eruption would be bad news.
It's unlikely that rich countries would experience famine as severely as poor ones and consequently they would probably still demand meat. Grain that could feed people would still feed livestock.
> Today we have a huge buffer from the large use of grain to feed animals.
This, plus the gigantic amount of agricultural land being used for biofuel production (almost as much as cattle food).