Earlier quoted context omitted.
It mostly does, yes. Nation is political. National cuisine and the claim of certain dishes, if official, are driven by government. See gastronationalism. You won't find Persian national cuisine. Iran however, yes, and it's mostly ethnically Persian. You'll find food traditions of other ethnic groups in Iran as well that aren't Persian. Iranian cuisine encompasses all of that within a political border.
I think you are conflating senses of the word, or rather you are defaulting to a very specific usage. There's the usage "Iranian national cuisine" which as you say is inherently political in nature because we mean "nation" in a civic and territorial sense, subsuming e.g. Persian, Azeri, Kurd cuisines, among others. There may be objections to specific inclusions or exclusions as we are considering Iran as a civic and…
Anyway. My point is that ethnic cuisine is not easily replaced by another term.