With a generous spirit and palpable affection for American values, Pope Francis won the nation’s heart during his six-day visit that ended Sunday. With his commitment to unchanging church doctrine, he disappointed some who yearn for reform.

His message was pastoral, a series of dramatic reminders of man’s obligations toward the needy, the stranger, the other. His gestures were powerful – his tiny Fiat that knocked the papacy down to a human level, his loving embrace of a disabled child, his decision to dine with the homeless directly after addressing Congress.

But as he delivered moving messages of humanity, the Argentine prelate, making his first trip to the United States at age 78, avoided engaging in America’s polarizing culture wars.

The result for many Catholics, liberal and conservative, was a sense of possibility and renewal, tempered by questions about whether welcoming rhetoric is enough to bridge serious divisions as a traditional church struggles to find its place in a fast-paced, disillusioned society.

“This was a real feel-good visit,” said Jeannine Hill Fletcher, a feminist theologian at Fordham University in New York. “He called us back to charity in a really beautiful way. But look at the missed opportunities to deal with the complex issues that divide the Catholic Church in America. Where was the open discussion of the places where the church is really wrestling? Where were the realities of women, the realities of gay and lesbian Catholics, the realities of racism?”

For some Catholics, Francis’s decision not to speak explicitly about the pressures for reform in church policy on divorce, abortion, contraception or homosexuality was what allowed him to connect to people on more foundational questions of faith and hope.

“The open question of this papacy,” said R.R. Reno, editor of the conservative Catholic journal First Things, “is whether the atmosphere is encouraging or the unrealized hopes are discouraging. Many Americans are spiritually exhausted by the culture wars, and in him, they feel a relaxation of those wars. I’m a conservative Catholic and I find him very appealing, but he has raised expectations of change that are not going to be fulfilled.”

Again and again in speeches before Congress, at the United Nations and at Masses and meetings in Washington, New York and Philadelphia, Francis sent a dual message: His notion of Catholicism offers open arms and declines to be the harsh Church of No that has turned off millions of American Catholics, but the church is an eternal institution and its doctrines do not change to conform to contemporary social trends.

“This visit is a breath of fresh air,” said Timothy O’Donnell, president of Christendom College, a Catholic institution in Front Royal, Virginia, “because he’s connecting people to things that are timeless, fundamental truths. People get it when he talks about the Golden Rule – the true, the good and the beautiful. Americans do tend to try to put people immediately into categories of our politics – left and right, liberal and conservative. This pope doesn’t fit into those categories. Rather, he brings people together.

“He has the common touch and the humor – look at his offhand comments about mother-in-laws,” O’Donnell said, recalling the pope’s crack Saturday about how families often quarrel: “Plates can fly and children give headaches,” Francis said. “I won’t speak about mothers-in-law.”

But one person’s joke is another’s slam, and Fletcher saw that moment as evidence that the pope is out of touch with a changing world. “The pope doesn’t have a mother-in-law,” she said, “but he can invoke the hostile humor of the mother-in-law joke that devalues women. His tone says he’s trying to take the church in a new direction, but where were the challenging questions? He listened to the victims of sexual abuse as a pastor, but where is the anger we need to feel at a church that was structured in a way that allowed this violation to occur?”

The pope’s meeting with a handful of abuse victims Sunday, and his statement that abuses of children by clergy are a “crime,” were evidence of an effort to confront the scandal. But to many advocates for abuse victims, Francis fell short, failing to commit the church to transparency about who committed abuses and how they are being punished.

Francis’s agenda was designed to focus less on church policy and more on large questions of faith and modern life. “This was a generous trip, a cautious trip,” Reno said. “Anyone who wanted him to confront the ills of America would be disappointed. There are plenty of conservative Catholics who wish he’d been more strident on abortion. He steered clear of our debates about single-sex marriage. It was a deliberately non-confrontational visit.”

He is, like the United States from its revolution to today, a sunny pragmatist with clear, bedrock principles.