Several of the crops most strongly identified with particular countries arrived there comparatively recently from elsewhere. The pattern is consistent, and the reasons are agricultural.
Crops were adopted for yield and reliability
Farmers choosing what to plant were solving for calories per area, resistance to failure and suitability to their soil and rainfall.
An introduced crop that outperformed a native one on those measures was adopted quickly, regardless of how long the native crop had been grown.
Cultural attachment then followed the crop that fed people, rather than determining which crop was planted in the first place.
New crops often filled a gap rather than replacing anything
Many introductions grew where existing staples could not, on poor soils, at higher altitudes or through a dry season.
That made them additions rather than substitutions, and they were valued precisely because they produced food in conditions where nothing else would.
Crops adopted in that role tend to become associated with the poorer regions that needed them most, and their cuisine develops around them.
Cooking traditions adapted rather than being invented
A new starch was generally treated using the methods already applied to the old one, so it entered the cuisine in a familiar form.
Over generations the methods were refined to suit the new crop's properties, and the resulting dishes came to seem original to the place.
This is why an introduced crop can be central to a cuisine's most traditional-seeming dishes without those dishes being especially old.
Preservation and processing had to be worked out locally
Some introduced crops require processing to be edible or storable, and the methods for doing so had to be developed or transmitted alongside the plant.
Where that knowledge travelled with the crop, adoption was smooth, and where it did not, the crop was used badly for a period before the technique caught up.
These processing methods often became the distinctive element of the local cuisine, more so than the crop itself.
Identity forms faster than people assume
A few generations of a crop being the everyday food is enough for it to be experienced as traditional by everyone alive.
Written records rarely survive at household level, so the memory of a staple's arrival fades quickly and only trade documents and botany preserve it.
The result is a world where national dishes routinely depend on crops that arrived from another continent, which is a more accurate picture of how cuisines actually form.