The main reason people go to fast food restaurants is financial. For evidence of this, you need only look at the advertising campaigns by these establishments, which usually brag about $1 menus and the like. If you take a trip into a Burger King, McDonald's or Carl's Jr., you'll often see a mix of people on the go and homeless people.
I'm not really sure what the economics are, but I'm not convinced that the absence of fast food restaurants in low-income areas will in any way bring down the price of food at other establishments. In fact it may raise it as there will still be a high demand for food and suddenly fewer establishments available to sell goods at affordable prices. It's doubtful that very many unintended consequences were considered when the L.A. ordinance was passed. Feeling good and morally active is usually the top objective of these sort of actions.
From a Slate article by William Saletan:
What we're looking at, essentially, is the beginning of food zoning. Liquor and cigarette sales are already zoned. You can't sell booze here; you can't sell smokes there. Each city makes its own rules, block by block. Proponents of the L.A. ordinance see it as the logical next step. Fast food is bad for you, just as drinking or smoking is, they argue. Community Coalition, a local activist group, promotes the moratorium as a sequel to its crackdown on alcohol merchants, scummy motels, and other "nuisance businesses." An L.A. councilman says the ordinance makes sense because it's "not too different to how we regulate liquor stores."
What the councilman doesn't take into account is that, by banning the sale of certain foods, food zoning steps into a whole different territory than alchohol or cigarette regulation. Alchohol and cigarettes are vices. Food is a necessity. If this were to expand into the sale of unhealthy foods in grocery stores, which is possible, Los Angeles would really be stepping into a new frontier of government regulation.