The Independent Inquiry into Child Sexual Abuse (IICSA) is examining the prevalence of paedophilia in the English Benedictine Congregation and failures in protecting young people.
This will focus on offenders that targeted children at two Roman Catholic schools, Ampleforth in North Yorkshire and Downside in Somerset, over the course of many decades.
But although numerous inquiries have exposed the problem of child abuse within church institutions and a string of offenders convicted, lingering safety concerns could remain, it was heard.
Counsel to the inquiry Riel Karmy-Jones told a hearing at IICSA's headquarters in south London: "It may be that during the course of evidence and the submissions to come (that) there is some acceptance of failings, but reliance will be placed on changes that have been made over the years.
"But, as you will hear, concerns remain and you are likely to hear evidence that suggests safeguarding problems are still ongoing, in some instances, and with the inevitable result that children may remain at risk."
The Roman Catholic Church is one of 13 arms of public life being scrutinised for child safety failings by IICSA.
Turning a blind eye to paedophilia should be made a criminal offence so Church institutions are discouraged from hushing up scandals, a victims' lawyer said.
Richard Scorer, who represents 27 core participants to the inquiry, said some Catholic Church schools concealed offending out of concerns for their reputation.
Many rely on private school fees to survive and cannot risk exposing misconduct, turning schools into "honeypots where multiple offenders operate", he said.
"The reputational pressures, the cultural and theological factors which led to abuse being covered up in Catholic institutions have not gone away," he told the hearing.
"They remain as powerful as ever."
Such episodes have happened "over and over again with the Catholic Church" as those who assist in the cover-up face no consequences, he said.
This leaves whistleblowers with "no real lever" to enforce complaints, the inquiry was told.
Addressing the inquiry chairwoman, Alexis Jay, Mr Scorer continued: "Madam, because we have no mandatory reporting law, that temptation to cover up, in our view, remains undiminished today.
"The Catholic Church and the institutions you hear from in these hearings will tell you that things are different now.
"But the question you have to ask is this: when all the fuss from this inquiry has died down, can we really rely on these institutions voluntarily to ensure that they never slip back into old habits, even though the old temptations exist today as they surely did before?"
In her opening statement, Ms Karmy-Jones outlined many instances where church officials chose to keep abuse quiet.
A "wide spectrum of behaviour", ranging from rape to voyeuristic beatings, was inflicted on school pupils over many years, she said.