>Those things weren't created primarily to give people work

They absolutely were.

They were created under the auspices of the Public Works Administration (originally Federal Emergency Administration of Public Works) - part of the 1933 New Deal:

https://www.archives.gov/research/guide-fed-records/groups/1...

"Functions: Administered a comprehensive public works program to promote and stabilize employment."

>If no one needs to commute to work in Manhattan, then there is no need for a Lincoln Tunnel. If no one has business meetings or disposable income for leisure travel, then LAX and LaGuardia would be idiotic.

That does not change the fact that these infrastructure works were created primarily to give the unemployed jobs and wouldn't have existed without it.

>We do see this kind of stuff - huge infrastructure projects with no users - in China.

Some of the infrastructure is like that but most has enough users to justify its existence. Their infrastructure-building binge isn't crazy. Our intentional lack of infrastructural improvement (which is entirely about artificially throttling employment and wage growth) is crazy.

Even if they were created to give people work, what is wrong with "we might as well get something useful out of this untapped unemployment"?

Define "useful" to your heart's desire, be it Hoover Dam 2.0 or Snowflake Poetry.

Examples of work more for work's sake might be landscaping or cleaning up streets. There are loads of rest areas or urban median strips/verges that look really awful worldwide. We could easily give people some responsibility for maintaining those.