Lincoln Heights public housing in Washington, D.C., in 2013. (Michel du Cille/The Washington Post)

MUCH HAS been made of a New York family paying $1,574 a month to live in public housing while earning $497,911 a year. The case, which the inspector general for the Department of Housing and Urban Development unearthed, is as “egregious” as the watchdog said in a report. Yet the real problem is not the relatively small number of tenants who earn more than they are allowed; it is the much larger number of people on the waiting list for housing.

The inspector general’s report revealed that more than 25,000 families living in public housing had annual incomes that exceeded HUD’s housing assistance eligibility level. It highlighted a handful of other cases like the one in New York, where households with enough income to afford the market rate for a house or apartment live instead in subsidized units, leaving people who really need housing scrambling for a place to sleep.

Since the report’s release, HUD has switched course and vowed to evict more tenants. The department’s initial reluctance was understandable in part. Most “over-income” tenants, the report found, were within $10,000 of the threshold — hardly able to make it in the market. Kicking out a family newly on the upswing might send it spinning downward again. There’s also a case to be made for income diversity in housing developments. Developments where there is some mix of income are less vulnerable to crime, and those who have risen or are rising out of poverty can set an example for other residents.

But while evicting those who have just gone over the eligibility limit may not make sense, HUD should not turn a blind eye to all tenants who make more than the rules allow. Housing assistance wait lists in some cities are more than 100,000 people long. HUD could encourage above-threshold tenants to make room for needier applicants by telling all local authorities to raise rents based on income. Some tenants — perhaps the best off — might leave. Others would stick around, as long as the cost remained below market level.

Even that, though, is hardly an answer to the country’s public housing woes. The 25,226 families the HUD inspector general found were above the income limit are only 2.6 percent of the total living in subsidized housing. Many more are on wait lists for homes, and others are on wait lists for Section 8 Housing Choice Vouchers that are just as long.

Affordable housing programs need more money to revamp old units, build new ones for mixed-income use and provide vouchers generous enough to get people out of bad neighborhoods and into better ones. Otherwise, wait lists will not go down, and those on them will have no chance to make their way up.