'critical responsibility' is correct and usable in written English. You can use it when referring to a responsibility that carries a great level of importance. For example, “The government has a critical responsibility to ensure the safety of its citizens.”.
His standard of critical practice and his model of critical responsibility are awe-inspiring.
Park has the difficult but critical responsibility of diffusing threats from the ever-combative North Korea.
But he reserved his sharpest words for the Palestinian Authority, which he said "bears a critical responsibility for halting the terror through immediate and decisive action".
Planning has played a transformational role in improving the quality of life of all of our communities and has a critical responsibility to tackle poverty.
While some of these stories might sound amusing, they do lead us to ponder the implications of a future where robots and artificial intelligence take on more critical responsibilities and will have to be held responsible for the possibly wrong decisions they make.
Re "Schools Expect Law to Require Private Tutors at City Sites" and "Mayor's Promotion Standards Are Approved for Fifth Grade" (news articles, Sept. 28): To whom will the Department of Education entrust the critical responsibilities of tutoring our "failing" New York City public school students?
One of a defense attorney's most critical responsibilities is to advise a client regarding the sentence he might face after a trial, and to give dispassionate recommendations regarding any resolution offered by the prosecutor.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com