The phrase 'engrained in' is correct and can be used in written English.
For example, "The idea of helping others is engrained in my family's culture."
"It's less engrained in a vague message and more engrained in policy and values specifics".
But humiliations were engrained in daily existence in countless ways.
That is how misconceptions can become engrained in public opinion.
John Christensen of Tax Justice Network said: "Tax avoidance is deeply engrained in Britain's corporate culture.
But even more engrained in soccer is Brazil, which has won the World Cup five times.
Proprietary algorithms provide a competitive edge, so secrecy is engrained in the culture.
More important, the specter of his condorlike wingspan on defense was engrained in Kansas' psyche.
Its morals and songs are engrained in my soul, so Salzburg is my frothy mecca.
The fascination of black bodies remains deeply engrained in western culture's fantasies.
The stereotyping wasn't just his; it was engrained in the culture, a chronic condition.
But beyond appearances, her deep conservatism is engrained in all aspects of her politics.
