Research has compared a healthy meat diet to a healthy veggie diet. It was found that the vegetarian diet was the healthiest. Some vegetarians would eat meat in this situation, others wouldn't. However, the chances that we would find ourselves in this situation are so slim, it would be up to the individual to decide what to do. Protein is available in all foods other than refined white sugar.
Meat does provide protein, however, it is only one source.
Pulses such as beans and lentils contain high levels of protein, nuts are also a good source. Some people do change diets as they may change fashions. However this fashion has been around for thousands of years and is spread globally. Vegetarian dishes in restaurants tend to be lower priced than most meat dishes. However, cooking food from the raw ingredients does tend to be cheaper.