Little Ceasar’s has often failed and closed MANY MANY stores that were not profitable. Not only do they have a food cost advantage (both buying power and the use of low quality goods) they also have a marketing advantage. You would have to spend about 6-8% of sales on local marketing to match them which really can not be done at $8 prices. As pointed out above, LC does not go into markets this size.
I am not familiar with all the independent businesses around the nation, perhaps others on this board are, but I can not think of a successful example of the model being proposed. I can, however recall a number of stories posted here about low price indy stores that went out of business and were re-opened by new operators that changed the name and the price structure after buying the assets for pennies on the dollar.
Further, starting with this model takes away your flexibility. It is very difficult to go from a low price model to high price if it fails, not so the other way around.
Food cost is climbing; 14" cheese pie cost for delivery or carryout costs me a little over $2. Adding in spoilage, condiments, paper goods, cleaning supplies, waste etc you can maybe do 30% food cost at these prices on the goods you sell but I doubt it. Adding in mistakes, donations, etc etc it will be impossible. Labor is getting tighter almost everywhere too. I know I am in a high labor market, but wages are rising and will continue to do so. Same for all forms of fuel for cars, ovens, refirdgeration.