In the Reagan era, the idea of a political vision centered on children influenced many Democrats and some Republicans, including conservatives. As Democratic governor of Arizona, Bruce Babbitt declared 1985 “The Year of the Child,” earning mockery from The Arizona Republic for offering voters “quiche” rather than the “meat and potatoes” of Arizona politics, such as water rights and economic development. (A book called “Real Men Don’t Eat Quiche” was popular in the mid-1980s.) A National Commission on Children was started, where liberals and social conservatives such as Kay Coles James, now president of the Heritage Foundation, found common ground on an ambitious agenda that included a child tax credit and the children’s health program that Mr. Trump now proposes to cut. While the commission’s 1991 recommendations were widely derided as overly ambitious, most of them were enacted within a few years.

Kid-centered politics, in its first phase, was quite successful — at least if judged by the standards of whether it helped create programs that improved life for children, established some basis for bipartisan consensus, and in a few cases gave politicians an issue to run on. CHIP funding, for example, was a winning issue for Democrats in both the 2006 and 2008 elections, and restoring funding for the children’s health program was one of Barack Obama’s first moves in the White House. Between 1980 and 2010, funding for children’s programs more than tripled, in current dollars, according to the Urban Institute’s annual “Kids’ Share” report.

For all that success, children-centered politics alone didn’t quite live up to Mr. Greenberg’s promise of its transformational power. Kids didn’t open the door to a broader recognition of the value of government. They don’t force voters to confront the imbalances of power in the workplace and the larger economy that have led to stagnant or declining wages for the majority of working families. Those underlying conditions limit life chances for children, as well as for young adults and parents, in ways that government redistribution programs can’t compensate for. Children can be carved out, as a kind of special vulnerable category, without challenging the underlying structures that lead to inequality.

A focus on children could even be, and was, compatible with the sort of business-friendly and Wall Street-friendly politics that Democrats adopted in the Clinton era — the very brand of politics many young Democrats are eager to relegate to the past. Democrats of the current era, including most of the prospective 2020 presidential candidates, are unlikely to be satisfied with a political language that focuses mainly on children. They’re on to bigger ideas that get to the core of the economy and fairness, like a job guarantee or universal basic income. Even universal child care seems to have slipped from the agenda.

There’s also a dangerous strain of kids-first politics, one that focuses on the relative benefits of programs for the elderly and disabled, Social Security and Medicare, compared with those for kids. That makes sense if the only resources to increase benefits for kids could come from those programs rather than, for example, closing the tax loopholes for private equity.