I had an apartment during my junior year of college. There was a guy there that smoked barbecue on his patio. I soon learned a tasty sandwich could be had for the right price. 
The guy had a nice side income for awhile. Eventually somebody reported him and I heard that the Health Dept read him the riot act. Ending my supply of late night sandwiches.
A shame because they were very good. I recognize there was a slight risk but barbecue is a well cooked meat. I never had any concerns.
Also, the food is all just extruded seaweed meal pressed into different shapes and colors.
I don’t mind a industrial-type kitchen, basically along the lines of a large-scale catering operation, running a delivery-only operation. (I’m assuming the kitchen would be subject to health and safety inspections). I would mind if they pass themselves off as different restaurants with their advertising and copy, especially if they pass themselves off as mom-and-pop or small authentic ethnic joints (“Diego had a dream when he came to America: To recreate his Tia Rosa’s famous Baja fish taco recipe.”)
The only way I’d mind if they rebranded themselves is if that made it harder for me to avoid them if I thought their food was crap. Otherwise, branding is just business, and I don’t care.
bmoak: Do you care if a dine-in restaurant lies about its history? Like how Einstein Bros Bagels pretends to a history from the 1890s when it was founded in 1990?
Branding is one thing. I wasn’t clear in my post, but the OP laid out a situation where the central kitchen is branding itself as multiple restaurants, with my caveat that the central kitchen is branding itself as multiple small mom-and-pop and/or authentic ethnic places when it is the same people making all the food in the same kitchen with the same supplies off the Sysco truck.
I don’t think much of places that make up a fake backstory, unless it was done in an obviously tongue-in-cheek manner.
We tried it in the prison system. We had the huge food production operation in Elmira (it was listed in the Guinness Book of World Records as the largest kitchen in the world). Every week they would make hundreds of thousands of meals and chill them down to just above freezing. Then they’d load them up on trucks and ship them out to all of the prisons in the state. At the prisons all we had to do was heat and serve.
It didn’t last. It turned out it was cheaper to decentralize the system rather than run it all out of one place.