Food replicas were first made in 1923. A department store in Tokyo asked a workman to make these wax replicas in order to have the customers chose their menus before getting inside a restaurant. and raise their turnover. Instead of having the actual food displayed, they are superior in a way that they are cheaper and more sanitary. For those merits, many restaurants started to use the food replicas for their display.
Today, you can find many of them displayed inside a mall or a normal restaurant in Japan; it is very common. It is probably not too much to say that these food replicas support Japanese restaurants.