That's not entirely true - if it were, most food would be grown in the tropics. Some climates suit some plants better than others.

You might get some benefits from a suitable climate moving into a fertile area, but equally you could get disastrous impacts from a suitable climate moving away from a fertile area.

You can see the impact of increased intensity of weather events on food availability already, for example, the horseradish crop failure this year means Burger King is out of Zesty Onion Dip until spring: https://dailygreenworld.com/2019/11/22/earth-changes/climate...