Extremophiles: a special or general case in the search for extra-terrestrial life?

Since time immemorial life has been viewed as fragile, yet over the past few decades it has been found that many extreme environments are inhabited by organisms known as extremophiles. Knowledge of their emergence, adaptability, and limitations seems to provide a guideline for the search of extra-terrestrial life, since some extremophiles presumably can survive in extreme environments such as Mars, Europa, and Enceladus. Due to physico-chemical constraints, the first life necessarily came into existence at the lower limit of its conceivable complexity. Thus, the first life could not have been an extremophile; furthermore, since biological evolution occurs over time, then the dual knowledge regarding what specific extremophiles are capable of, and to the analogue environment on extreme worlds, will not be sufficient as a search criterion. This is because, even though an extremophile can live in an extreme environment here-and-now, its ancestor however could not live in that very same environment in the past, which means that no contemporary extremophiles exist in that environment. Furthermore, a theoretical framework should be able to predict whether extremophiles can be considered a special or general case in the galaxy. Thus, a question is raised: does Earth's continuous habitability represent an extreme or average value for planets? Thus, dependent on whether it is difficult or easy for worlds to maintain the habitability, the search for extra-terrestrial life with a focus on extremophiles will either represent a search for dying worlds, or a search for special life on living worlds, focusing too narrowly on extreme values.