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Separate from my other reply to you, answers to your title question and final question, since they're two different things.
Title question: Governments, in general, do not "benefit" from performing the functions they are legally required to perform. They just do those things, because it's what the law says. Criminal justice, armed forces, infrastructure...the law says to do those things, so they do. Which leads us to...
Final question: The law says to do that because legislators wrote those laws, and the legislators wrote them (generally) because they promised their voting constituents that they would do so. Some nations it's rather more complicated (e.g. China), but the net effect is the same: people in general STRONGLY support pension laws, so pension laws exist, and governments follow them.
It's really not hard to see why, as I answered in my other comment. "The best-laid plans of mice and men oft go awry," to use the English version of Robert Burns' poem. Having a near-guaranteed safety net (nothing is ever *absolutely* guaranteed) is a huge priority for many who want to live with at least some comfort when they're old.
There's nothing here!