The reason is that the overwhelming majority of the budget is spent automatically - pensions, medicare, social security, and all of these expenses are unavoidable and in a mandatory expenses category. The remainder of the budget, including military, is considered discretionary. That discretionary spending is the thousands of pages that Congress creates (and fails to read) each year. And it's in that budget that most of the things we associate with government came from - everything from education, to roads, to infrastructure, and also the military.
So by the numbers in 2024 the discretionary budget was "only" $1.7 trillion and after military spending "only" $900 billion was left. "Only" obviously needs to be in quotes but that's indeed only about 13% of the e.g. $6.7 trillion total budget in 2024. And so each time you cut something the amount of money left for the things we generally associate with government skyrockets. So for instance USAID was "only" $50 billion, but that was more than 5% of the entire discretionary budget!
US Federal Workers cost $293 billion [1], and contractors amounted to $760 billion. This is excluding secondary costs/benefits, which are extremely high for government workers, and only direct payments. It also excludes budgeted expenditures that would have been performed by those employees. So that's already $1.05 trillion and we're clearly substantially lowballing the figure. Yet that's already more than the entire discretionary budget excluding military, and certainly far more than 4% of the entire budget (as would be required for cutting 25% to only result in a 1% cost saving, as proposed).
[1] - https://www.afge.org/article/afge-continues-to-debunk-miscon...