Food production is indeed a solved problem in most countries (we are almost post-scarcity when it comes to food), which is why obesity is a much bigger issue than hunger today. Hunger is present pretty much only in conflict zones. I fully expect such issues in conflict zones, even in AI post-scarcity world.

Housing is definitely not post-scarcity today, building a house is still very expensive, not to mention the limited availability of land zoned for housing.