It’s somehow fitting that the mayor who finally finished what John Lindsay started at the Chelsea Recreation Center was Michael Bloomberg. Lindsay was the liberal Republican whose spending brought the city to a fiscal crisis and a middle-class exodus. Mr. Bloomberg is the liberal Republican whose tax increases have made New York the city with the highest state and local tax burden in the nation.

Part of the reason it took 36 years — since the Lindsay administration — to finish the center is that the mayors in between realized that providing treadmills, stair-climbing machines, stationary bicycles and an indoor swimming pool in Chelsea wasn’t exactly the highest priority in a city with a lot of other needs. Not that bicycles and swimming pools aren’t nice. But there’s a temptation in New York City government to provide everything that might be nice, without stopping to think about whether the service might be more efficiently provided by the private sector.

As it is, Chelsea is crawling with gyms. There’s a New York Sports Club at 23rd Street and 8th Avenue. Chelsea Piers, on the Hudson, has a pool and plenty of other workout facilities. The McBurney YMCA has an indoor pool and it’s also nearby. Bally’s, David Barton, the Chelsea Gym, the American Fitness Center are all either in the neighborhood or a few blocks away. Yet the city’s taxpayers just spent $22.4 million to compete with these facilities. The $22.4 million represents only the capital cost of the new recreation center. It will no doubt cost the taxpayers millions more over the years to pay the staff of this facility and to heat, clean, light and maintain it.

Yes, we know that many of the children who will use the recreation center may be too poor to afford the privately operated facilities. And yes, we know that obesity is a public health problem. But you don’t hear the advocates talking about subsidizing gym memberships for Medicaid recipients, because that might involve working with some actual private companies. It wouldn’t necessarily be a bad idea.

Chelsea has its share of housing projects, which were built before people realized that instead of building government housing for the poor the government could pay for vouchers that the poor could use to rent apartments from private landlords. The Chelsea Recreation Center is a kind of housing project for exercise. It’s a case of the government getting into the business of providing something that the private sector already is doing a fine job of providing.

As it is, New York is straining under the burden of a bloated public sector. If we had the lowest state and local tax burden in the country, or if our taxes were somewhere in the middle, maybe it would make sense to spend money on government gyms. If our other priorities were all taken care of, it might make sense, too.

But Mr. Bloomberg is claiming that our public schools need more money from Albany. And we wouldn’t be surprised if the new Chelsea Recreation Center is open for longer hours than some of the city’s libraries, which have absorbed cuts in recent years. So with all the city’s needs, the idea of opening this indoor pool at taxpayer expense strikes us as all wet.

It’s not only Mr. Bloomberg’s fault. The Giuliani administration restarted this project, and plenty of Democratic politicians have shepherded taxpayer dollars toward it. But Mr. Bloomberg, like Lindsay before him, is the mayor.