The phrase "a deep problem in" is correct and usable in written English.
It can be used to describe a significant or complex issue within a particular field or context.
Example: "There is a deep problem in the education system that needs to be addressed urgently."
Alternatives: "a profound issue in" or "a serious challenge in".
And yes, the demonization of those who disagree with us is a deep problem in U.S. politics.
He spoke of a "deep problem in Islam," of a world in which "life doesn't have the same value it does in the West".
Michael Gove said the sheer scale of privately educated men in positions of power in business, politics, media, comedy, sport and music was proof of a "deep problem in our country".
Members of Congress, led by Senator Glenn and Representative Thomas A. Luken, an Ohio Democrat, said the department's refusal to release the data was part of a deep problem in which the agency responsible for producing radioactive materials was the main source of funds to study radiation's health effects.
The fact is that there is a deep problem in America and it didn't start with Donald Trump, or his alt-right surrogates.
A deeper problem in these incentive contracts is the effect on investors' risk taking.
But they may point to a deeper problem in the Court, says Dahlia Lithwick in the New Republic.
After a few days, the first question sparked more: Was there a deeper problem in the counterinsurgency campaign?
But sometimes it's a symptom of a deeper problem in your culture, product, or operating model.
But there's a deeper problem in the whole notion that what this nation needs is a successful businessman as president: America is not, in fact, a corporation.
Their absence is a sign of a deeper problem in the book: there is a conspicuous absence of physical and emotional intimacy.
