Imagine what would happen if everyone did what the author did. The system would collapse. I think you put a wrong diagnosis that the author couldn't possibly affect the administration. Maybe not much, maybe there was only a chance, but statistically he did put some pressure on that organization.

More likely they'd just cancel the benefits.

If everyone did it the managers would screech for more money, more headcount, and maybe get it. Worst case the employees are in the same position as before, best case the management is richer and more powerful and possibly some of the current workers become low level management over the new employees. It is doubtful they would try to make the process smoother/easier/accommodating because that would remove the method by which they can gain more power and employees. To see this in action note how agencies are constantly burning up all their budget even if they don't use it so they can justify as much or more the next year, if they have extra time/money they will invent something to justify not giving it up.

Government works the opposite of industry. In industry you win power/prestige/money generally by getting more profits which usually means making needlessly inefficient process less so (although in large company with multiple layers of middle management this can become completely decoupled). In government there is no concept of profit so you win more power/prestige/money by having more headcount and paperwork to shuffle around which justify your existence.