From what I can gather, when capitalist democracies cut government departments, they just end up outsourced to private companies who reap whatever infrastructure was there and replace it with their own, cheap and barely functioning version for profit.
So basically the government service is still there, it’s just privatised and crappier.
The government gets bigger directly under capitalism as well. Graeber points out in Debt that the number of people working in the government in Russia more than doubled after the fall of the Soviet Union than right before it fell. It’s all grift