However, all the life we know of is part of the same Earth system. Just because some extremophile exists in a freezing desert or boiling pool does not necessarily mean that the same environments on other planets would have those organisms.

Life on Earth evolved and spread under specific conditions - our gravity, sun brightness, geology, magnetic field, large moon, etc etc. It then spread to all possible environments on the planet and evolved to live there.

Unfortunately, it could be that the 'growth conditions' for life are quite specific even if - once it gets going - life can evolve to more general environments.