Earlier quoted context omitted.
They could also make it reservations only, and control their price and speed.
Making a burger joint reservations-only changes the character of the service significantly. Imagine Twitter saying "We're scaling too fast for our backend to keep up, so we're going to require reservations a day in advance before you tweet so we can throttle the number of requests."
I can guarantee you there are famous NYC restaurants in my neighborhood where I can get a table even if there are lines out the door or reservations are completely full.
You just have to live in the neighborhood and actually put some effort forth to introduce yourself to staff and maybe go occasionally when you know it will be slow (like during a snowstorm or holiday). It does require a good manager/host though.