Almost all depictions and descriptions I see of kitchens (of at least moderately wealthy families with multiple-room houses) from the 1800's up to the early 20th century show them as rooms where the actual work of cooking is done but no entertaining or actual eating would have happened. By the mid 20th century and onwards they seem to have gotten bigger with more thought to their design as a place for gathering as a family or for entertaining.
Is this impression true and if so, how and why did this change come about?
Once upon a time, most kitchens were spaces for eating as social activity as well as for food preparation and cooking. The modern architectural term for this kind of multi-use space, "farmhouse kitchen", reflects the peasant origins of this type of kitchen. The functional centre of the kitchen, important to both the cooking and social uses, was the hearth or fireplace. Food was cooked over an open fire, either in cauldrons or pots suspended over the fire, or in pots placed on the fire, or roasted by the fire. The fire was used for cooking, and also provided light and heat for the living space. Often, the fire was central to both indoor activity and the design of the house (e.g., Iron Age roundhouses with a central hearth). Many houses consisted of a single room, which often thoroughly integrated the kitchen into indoor activity.
There were exceptions. One driver of the exceptions was that open fires have disadvantages: the heat they provide can be undesirable when it is warm, and they produce smoke, and can be fire hazards. Depending on the local climate and weather, cooking could take place outdoors, or the kitchen could be separated from the rest of the living space. Some European peasant houses consisted of two rooms - one for the humans and one for the animals, a half-house, half-barn design. In some cases, the hearth/fireplace was on the animal side of the house, perhaps placed against the wall separating the two halves, so that it would still provide warmth in winter. Kitchens were sometimes exiled to outbuildings, to reduce the risk of fire.
For the wealthy, there were further factors pushing the kitchen away from the living spaces:
The wealthy could afford large homes where the kitchens were separated from the living spaces.
The cooking and other kitchen tasks were done by servants or slaves. The kitchen was a workspace. It would have made no more sense to entertain guests in the kitchen than to entertain them in a carpentry shop.
Even after the introduction of chimneys, there was still noise and smell (smoke and cooking smells). Better to keep one's distance!
For poorer people - the peasant/working classes - there might be no choice. If the home is a one-room house or apartment, the cooking will take place in that room. Sometimes, there was a choice, and the home might consist of a few rooms. One of these would typically be a small kitchen. Often, "small" was an understatement - with no servants to cook, the kitchen was often just big enough for one person to work in. This especially the case for urban kitchens - rural kitchens, as the modern "farmhouse kitchen" suggests, often had more space available. The small size of many urban kitchens was also possible because a smaller range of cooking and food preservation tasks were needed (food could be purchased already cooked, there was no need to preserve and store the produce from the garden and fields, etc.).
The modern multi-purpose kitchen is largely a meeting of these lower-class and upper-class traditions, in new styles of middle-class kitchens. One kitchen-relevant thing that the middle-classes lacked was the dependence on servants. The cook - typically the wife/mother - was expected to do most of the work in the kitchen. This was helped by new facilities and appliances becoming available: running water made many tasks easier, refrigerators could simplify shopping and food preservation, and modern gas and electric stoves reduced smoke, noise, and the need to carry coal or split firewood. Many of the new appliances were marketed as status symbols, signs of modernity. Their expense could also inspire pride in ownership. This reduced the costs of integrating the kitchen with the rest of the living space, and also provided the benefit of showing off one's modern kitchen.
The other key step in the evolution of the modern multi-purpose kitchen was the growth in housing space - suburban sprawl allowed large houses (compared to urban apartments), and allowed non-cramped kitchens. (There's a science to designing effective tiny kitchens, from the famous Frankfurt kitchen designed in 1926 by Margarete Schütte-Lihotzky, to galleys on ships/boats (especially diesel-electric submarines!), and kitchens in mobile homes/caravans, etc. It's all easier when there's more space available - although the result can involve more walking and be less efficient.) The extra space allowed more counters and/or islands that could be used as informal dining spaces.
A driver of all of this was the growth in middle-class entertaining (perhaps a result of middle-class desire to emulate the upper-classes). This led to the opportunity to show off one's oh-so-modern kitchen, and, of course, to use it to prepare food to feed one's guests. A kitchen more integrated with the main living space allowed better interaction with guests during cooking, and there was a choice of either using the formal dining room, formal living room, or the informal space in the kitchen. There was no need to keep the kitchen as a separate enclosed space - open-plan designs offered easy interaction between people in the kitchen and adjacent dining/living rooms (and this was fashionable - Frank Lloyd Wright's "Usonian" houses often integrated the kitchen space with dining and living areas).