So let's take a simple example. If tomorrow the government decided it could offer the same level of education at half the cost but it meant laying off a lot of workers, would it do it?
Would? That's going to depend on the government, and who is controlling it. I think the question you really want to ask is:
should it?
To adequately decide the answer, however, we are going to need more data. Remember, one of the things a government should do is care for the welfare of the citizenry. If the government is doing a great job at that, through universal basic income, or some other measure that lessens the impact of that massive layoff, then yes, it should take the cost saving, and cut the jobs. On the other hand, if laying off all of those workers is going to have a significant impact on the welfare of the workers, than it should not cut the jobs until it can otherwise provide for the welfare of the workers who are now out of a job.
Contrast this with a business operating on a pure profit motive. That business is going to cut the jobs, thereby reducing their cost, but continue charging the consumer the same price.
The kind of psychology that it takes to be a very successful and wealthy CEO is most likely the kind of psychology that will produce a Stalin, Hitler, similar immoral sociopath as a political leader.