What is the structure? It is really hard to understand why they use the phrase "more than just".
It's not completely clear what you are asking but I think maybe you are confused with this because it's very common that people speak about fast food negatively with regard to nutritional value.
The sentence could easily be changed to:
fast food is about more than only nutrition
I'm guessing "just" is confusing you? Just is a way to say that something is not to the exclusion of other things. It can be replaced with only easily (usually). I can also say, "I just want to be friends". It has nothing to do with something being "just" in the sense that it's right or wrong or of noble value. It means, "I only want to be friends", in that particular context.
Just has a couple of meanings. It can mean something is noble or right. It can also mean that something is not to be singled out as the only thing. Or it can mean it IS the only thing.
I "just" want to be your friend.
means I "only" want to be your friend. But it does NOT mean I don't want any other friends or that I want you to have no other friends. Don't confuse those.
I'm not "just" your friend, I'm more than that too.
means I am more than a friend, I am more things than only a friend.
This is how the sentence is being used in your example. It's saying that for all the negative things we usually talk about regarding fast food, we need to consider more, because,
fast food is about more than "just" nutrition.
As for the the grammatical considerations, well, I'll leave those to the grammarians.
As for the meaning of the phrase "more than just," it is a shorthand way of saying, for example,
Regarding fast food, there are more considerations in play besides just nutrition. For example, there is . . .. [Fill in the ellipses with a list of other considerations or factors associated with fast food].
Using my imagination, I can think of several considerations regarding fast foods. Put negatively, they could include
the absence of joy in a home-cooked meal, enjoyed around a dining room table, with family and friends enjoying their repast and conversing freely about all sorts of thing
the cravings and habituation associated with many fast foods, including high salt content, high fat content, high sugar content, and instant gratification
the cost of fast food in comparison to the cost of a similar but home-cooked meal (in other words, economic considerations)
the sheer waste of resources, particularly the trash generated by consumers of fast food: paper, Styrofoam, condiment packaging, plastic, and more
the over-reliance on fast food, which obviates the need for experimenting with recipes for home-cooked meals
fast food encourages sloth with its convenience and speed, with very little effort involved (e.g. not having even to get out of a car to order, pay for, and consume the food)
On the positive side, fast food certainly provides employment for hundreds of thousands of workers and business owners and operators. There are probably many more positive aspects of the fast food industry, but from the tone of your exemplar sentence, the implication or connotation of the phrase "more than just nutrition" is that nutrition is not the only negative factor associated with the phenomenon of fast food. Hence the expression "more than just nutrition."