This is a current day narrative cast in events drawn from the past. However, and I was plenty old enough at the time to be tuned into the political reality, was not that the airlines were begging to shift the costs of airport security to the government, but rather that proponents of expansive government responsibility insisting that something as important as airport security could not be trusted to the private sector.

Consider this rather later statement from Sen. Joe Lieberman, one of the early proponents of creating a public airport security agency:

"Regrettably, some of my colleagues in the House and Senate are resolved to undermine TSA - and therefore airport security itself - by advocating for the pre-9/11 system of screening by private contractors. My response to that is: how quickly we forget.

Mr. President, we have already tried an aviation security system run by private contractors. It very tragically did not work. The 9/11 attacks did not occur because of one, two, or three specific vulnerabilities. They occurred because a number of our defenses - including our system of airport screening - were simply inadequate.

[...]

It became clear to many of us that aviation security was inseparable from national security, and we could not, and should not, rely on the private sector to do the job. The security of our skies would have to become a government responsibility. Americans need to be safe and secure wherever and whenever they traveled. And while I would not want to cast blame or criticism on any one contractor, we've already witnessed the results of a system utilizing private security companies which were constantly pressured to focus on costs first, and security second.", Senator Joseph Lieberman, Tuesday, February 7, 2012 [https://www.hsgac.senate.gov/media/majority-media/lieberman-...]

While that statement came later, it was very much in line with the argumentation in the immediate aftermath of 9/11 and was broadly supported by left and right. More at stake, reading between the lines, was much less to do with any corporate interests and more with congress just wanting to appear to be "doing something" in the wake of a national tragedy. Consider this more contemporary testimony from Rep. Nancy Pelosi:

"Since the attacks, steps have been taken to realign federal agencies and change responsibilities, the creation of the Department of Homeland Security -- another brainchild of the senator from Connecticut, Senator Lieberman -- and the Terrorism Threat Integration Center being among the most notable.

These may turn out to be worthwhile actions; however, my concern has been that these entities were instinctive responses -- although Senator Lieberman had suggested his department long before September 11th -- to general perception that things were not right, rather than a result of an exhaustive inquiry across the government with specific findings and specific recommendations for change", Rep. Nancy Pelosi, May 22, 2003, [https://govinfo.library.unt.edu/911/archive/hearing2/9-11Com...]

Trying to couch what happened with the nationalization of airport security as being a handout to corporate interests after the fact is like trying to demonize health insurance companies by saying that current day efforts to nationalize the health care system is really just an effort to give hand outs to big businesses involved in health.

Given how historically my friends in various progressive movements are so often advocates of precisely this sort of government assumption of responsibility; perhaps if the parent comment is correct in their assertion, then maybe we should be discussing how easily duped those same progressives are.

[EDIT: added Pelosi comment]