Yale University’s report on how to restore public confidence in America’s colleges and universities is full of smart and sensible recommendations. That’s not surprising when one sees the smart and sensible faculty who wrote it, led by the scholars Beverly Gage and Julia Adams. Among the suggestions: Reinforce the academic core of the university; don’t allow classes to be dominated by open laptops or other devices; do more to ensure that people do not self-censor; respect the ideals of free speech and academic freedom; “be human.” Although the committee doesn’t go so far as to say that nepotism in admissions should be eliminated (it asks only that it be reduced), it does suggest that Yale try to make its educational offerings free for a larger percentage of the population. Who would disagree?

It’s the recommendation to shrink the mission of the university that caught my eye. The committee claims that in 2016, “departing from its traditional emphasis on the creation and dissemination of knowledge, Yale expanded its mission statement to include ‘improving the world today,’ educating ‘aspiring leaders worldwide,’ and fostering ‘an ethical, interdependent and diverse community.’”

That is incorrect. It is true that Yale shifted its mission statement a bit in 2016, but the underlying ideal of cultivating people who would, as the language now says, “lead and serve in every sphere of human activity” had long been among the university’s goals. In fact, that cultivation has long been among the goals of many universities in the United States, adopted as these institutions sought secular replacements for their founding denominational creeds. Leaders of colleges and universities thought they had a duty to defend the freedoms that allowed higher education to thrive. My own school’s founding documents, written in 1831, spoke of furthering the “good of the individual educated and the good of the world.” We still cite that today when we speak of our mission to produce graduates who will use their educations to make a positive difference.

This is what the Yale committee wants to trim. “These are all worthy goals. But they are not what makes a university a university,” its authors opine. “At a moment when higher education is being buffeted from all sides, it is imperative to understand what we are here for and what universities do best. That requires clarity, not diffusion, of purpose.”

Amid the Trump administration’s ongoing attack on higher education, the message is clear: Don’t worry, it says, we are staying in our narrow lane. That’s not a mission; it’s a defense strategy. And the retreat from public purpose will not enhance trust; it will further erode it. A lack of public engagement and an air of cloistered privilege are a big part of why so many people now view universities with suspicion. Retreating further behind the gates will make a bad situation much worse.

Not all American colleges are viewed with distrust — community colleges, for example, still enjoy high levels of confidence, as do regional public institutions. The problem is with the attention-grabbing elite institutions. As the Yale report notes, they are far from blameless.

These institutions too often seem to offer lessons in condescension. Their faculty and students can appear to be better at moral posturing than at listening effectively to those with whom they disagree. Their campus cultures can breed premature and intolerant consensus, causing people to censor themselves for fear of being called out as having the wrong ideals. The need for more intellectual diversity in higher education is clear, except to those who believe that their exclusive club possesses a purity that other members of our society haven’t yet attained.

Most Americans understand that these elite schools give many wealthy people more opportunities to become even wealthier. They understand that the most popular career choices for Ivy League graduates tend to be consulting and finance and tech. Trust in finance is even lower than it is in higher education. Why should people trust the sector’s feeder schools? And why should they trust their admissions policies, with their opaque pricing structures and their pride in exclusivity?

Yale is one of the very few, very wealthy institutions that can admit applicants regardless of their ability to pay. Starting this fall, the university will charge no tuition at all to students whose families fall outside the richest 10 percent of the population. That’s an impressive step, one I wish my own institution could take. But the whole competitive admissions system at Yale and most other highly selective institutions — including my own — still favors applicants whose families could afford to expose them to private high schools, private tutoring and expensive résumé-expanding extracurricular activities, and who weren’t obligated to balance their calculus homework with the demands of an after-school job. As the committee notes, Yale admits fewer than 5 percent of its applicants. Unspoken is that probably three-quarters of them are qualified to attend and even get A’s, the average grade at the university.

The Yale committee calls for relying more on objective admissions standards such as standardized tests. The problem there is that those tests are anything but objective; the more colleges rely on them, the more the uncredited work of expensive tutors or test prep classes can distort the profile of the incoming class.

Expanding opportunities for affordable, high-quality academic experiences can make things better. That’s why recruiting a diverse class of students, with talented young people from areas of the country often underrepresented on elite campuses, is so important. The Trump administration’s war on D.E.I. makes this dangerous work, and so we should celebrate programs that bring college-level classes to underserved communities, such as those sponsored by Bard College and by the National Education Opportunity Network.

This cautious committee does call on the university to do more public programming, opening its gates even further to the communities around it. It also joins the national chorus for more programs in “dialogue across difference,” and I think it should be applauded for advocating civics instruction for all undergraduates. But these are small steps.

One can well imagine why a university committee might want to avoid provoking the ire of the Trump administration, which has hit higher education with more than a billion dollars of fines and has threatened schools whose campuses don’t seem to line up with its priorities.

But the ideals the Trump administration has been punishing are prerequisites for higher education to flourish — independent thought, a commitment to truth even when it’s inconvenient and a focus on the creation of truly democratic citizens. Endangering these ideals endangers the whole operation. Yale and other elite universities should find the courage to say so.