There's a reason outsourcing works.
It's easier to hire a business in a county that doesn't have a government that throws hissy fits for not getting as much of an increase in budget as they wanted from the previous year to turn a profit than it is to hire locally, where you have to support said government through each employee.
Governments don't care about profits. Most happily spend more than they make practically every year; it's called running a budget deficit, and it's something almost all governments do. In fact it's kind of the point of modern governments; if the government were to actually make a profit, that just means that the government is sitting on a pile of money rather than using it to make the country a better place.
No, there are two scenarios where outsourcing works (for certain values of "works"):
1) You are too small to rate a full-time employee in a particular field (eg. a small business outsourcing IT to a consulting firm), or the company you are outsourcing to can benefit from economies of scale that you can't by yourself (ex. service contracts for analytical instrumentation)
2) You are pulling a scam by externalizing costs, that is, you are:
2a) Externalizing infrastructure costs, as in dodging the taxes that keep the society around you functioning,
2b) Externalizing environmental costs, as in setting up manufacturing in a country that will let you dump toxic waste all over rather than cleaning up after yourself and relying on future generations to clean up your mess,
2c) Externalizing labor costs, as in setting up manufacturing/service centers in a country where workers have fewer rights, a lower starting skillset, and lower starting wages.
2d) Externalizing future capital outlays, as in getting a 1-2 year discount on this year's service, declaring a massive profit and giving yourself a huge 4th quarter bonus/boasting to the electorate about how much you saved them, knowing full well that in 2 years you'll have your golden parachute so you don't care about how much more the company will have to pay.
Governments rarely benefit from 1), and it certainly doesn't apply to airport security. In fact the opposite is true: the TSA can benefit from a nationwide scope that private companies can't hope to match. Local governments can benefit from 1, but mostly for small analytical contracts or by partnering with large multinationals (see City of Los Angeles outsourcing email to Google).
2a-2c pretty much don't ever apply to government outsourcing; that's more of a private industry thing. 2d is the big one, the big con job the neocons pulled off in the 2000s that saw us go from forecast surpluses to trillion dollar deficits inside of ten years. That's what government outsourcing means: it's a shell game, meant to give a politician a temporary political boost, at the cost of trillions of dollars to taxpayers.