TOPEKA, Kan. — For more than six years, Gov. Sam Brownback has steered Kansas on a hard right turn on one issue after another: taxes, guns, abortion rights, Medicaid and welfare benefits.

He will leave as an unpopular leader of a state in uncertain fiscal health, with more robust conservative policies and governed by a Legislature in which many in his own Republican Party have defied him. Polished, persistent and self-assured, Mr. Brownback has been seen as a model for the opportunities and perils of governing without compromise from the right on both social and fiscal issues.

But after the Trump administration said on Wednesday that Mr. Brownback, 60, would be nominated to serve as an ambassador at large for international religious freedom, his legacy in Kansas may be a cautionary note that even in a Republican state, there are dangers in governing too far to the right.

“He puts the lie to the myth that the default strategy is just to go as conservative as you possibly can in Kansas,” said Chapman Rackaway, a longtime observer of Kansas politics, now at the University of West Georgia.