We Fail Children.
The United States does a quite credible job of meeting the needs of senior citizens through programs like Social Security, Medicare, the Medicaid nursing home program, SSI, veteran's benefits, tax favored retirement saving programs, age discrimination in employment laws, and the Americans with Disabilities Act (whose beneficiaries are disproportionately the elderly).
But, the United States does a quite poor job of meeting the needs of children.
Poverty: Child poverty rates in the United States far exceed those of most developed nations, and our welfare system for them is relatively anemic.
Health Care: The Medicaid program for poor children is fraught with problems related to the fact that it expects providers to render services for far less than market rates provided by health insurance and Medicare. Almost all other countries have paid maternity leave while the U.S. does not. Drug research for children and pregnant women is discouraged. No health care system is more expensive.
Child Care: Child care and pre-school is expensive and the quality of these options is patchy.
Education: While the U.S. has many adequate public schools and a far number of excellent ones, a great many children (overwhelmingly poor and minority) are hellholes. No country in the world has a more costly system of higher education for students, with very protections for students from dishonest educational practices. Access to higher education is regulated mostly through the costly and damaging system of admitting students who aren't ready for their planned course and then flunking them out in short order.
Juvenile Justice: The United States routinely invokes the criminal justice system for misbehavior by children that doesn't warrant it, until recently was a global outlier that allowed life without parole and deaths sentences for juveniles, and still often imposes excessively long sentences on juveniles and makes grossly excessive use of solitary confinement for juveniles. Furthermore, the quality of due process for juveniles accused of committing crimes is deficient, and the secrecy in the court system surrounding the juvenile proceedings does more harm than good.
Abuse and Neglect: In most places, our system for identify and protecting children suffering from abuse and neglect seriously mishandles cases on a routine basis, and our foster care system is almost universally abysmal. For example, in the Denver Public Schools, homeless children are faring better than children in foster care.
Custody Disputes: Our court system does a poor job of handling parenting time and parental responsibility issues, which are frequently navigated by parents without lawyers who are grossly unqualified to do so; child support awards while much less haphazard than they once were and easier to collect than they once were tend to be miserly small (of course there are exceptions to every general rule), and custody decisions are made by a single judge with minimal familiarity with the family who has virtually unfettered discretion under a largely unelaborated "best interests of the child" standard.
Military Families: The U.S. military is pretty much the only employer in America that provides more compensation to employees (i.e. active duty military personnel) who have larger families than it does to single soldiers and to soldiers without children. in part because of this, a lot of young adults who have already started families join the military and a lot of young soldiers start families.
But, while it is relatively compassionate in this regard (although many low ranking soldiers with families are sufficiently low paid that they qualify for welfare benefits also), the military's record with military families is decidedly mixed.
Simply having policies that encourage and accommodate soldiers having families is somewhat problematic because the intrinsic nature of the job is that sailors on naval ships and soldiers deployed to foreign war zones must be away from families for prolonged periods which is a strain on families, which would suggest that policies that favor family deferral would make more sense.
Even when deployed on bases in the U.S. and in peaceful allied countries where families can accompany soldiers, the military's habit of constantly shuffling troops from base to base across the nation and world has seriously harmed generation after generation of military children.
Another issue recently identified is that military discipline directed at a soldier who commits adultery or mistreats his family frequently most hurts the soldier's family members whom the military conduct standards are designed to protect by economically harming soldiers upon whom they are economically reliant, discouraging families from reporting misconduct towards them and exposing them to abuse risk.
The military also provides inadequate care to veterans, particularly those with service related PTSD or other mental health issues, imposing a burden on their families.
One possible reason for this broad range of failures is that our democratic system, rather than failing to work as design, works too well. It rewards groups of people who regularly cast informed votes, and people who are able to devote time and treasure to the political process. Senior citizens do all of these things.
In contrast, children are, by far, the largest group of people who have no right to vote. Only the oldest are mature enough to devote time to the political process, and almost none have significant economic ability to advance political causes. And, less affluent parents of young children likewise tend to be short on time and treasure to devote to politics, are often ill informed about the process and candidates, and are not reliable voters. Children are a large and diffuse population with little means to self-organize. And, while their advocates in the form of school teachers, have an interest in promoting education funding, many other needs of children have few natural political advocates.
Utah is a notable case where the Mormon church institutionally and Mormon families who tend to have more children and to have children for more years of their lives, advocate more strongly for children than in most states, and that shows up in policy and budget decisions in a manner quite atypical of other states that are strongly politically conservative.
Institutions like mainline protestant churches that were once major advocates for children's well being, now have very few children as their congregations age and have declining institutional clout.
Admittedly, this is a weak theory, because while it is adequate to explain the American situation, it doesn't explain why the situation in different on many of these issues in other countries that also have a democratic process in which children do not vote. But, maybe it is a beginning.