In which state does the law allow health care institutions to withdraw life support when further treatment is judged futile

The answer is: California

The purpose of that law is to ensure that the fund for the support could be allocated to other people that have better chance of living.

The total fund for health care is very limited, and not all citizens are eligible to obtain the service that they need. When further treatment is judged as futile, pumping more money to the treatment would not bring any positive value to that patient. But, if it's allocated to other patient with higher priority, government's investment for that patient wouldn't become a waste.