I disagree. Big Government means the government getting into every subject possible. The opposite of this is that you have a government that only enters into essential matters for the well-being of society.
Which has poorly defined boundaries because people disagree on essential.
In practice "Big Government" is used only for PR value. It sometimes seems the more a politician or policy wonk uses it, the more they are actually likely to increase government spending when they are in power.
Most people seem to use "Big Government" to mean they don't like something the government is supporting or regulating, and "Essential Government Function" to mean something they want the government to pay for or regulate.
A void of power never creates a favorable outcome for the common person. If there's room for commercial activity in the area, you can expect all sorts of unethical tactics to eventually surface, like we see in cryptocurrency. In a free-for-all capitalism people will lie and scam and cheat for profit.
So I don't really know what could the government get out of that would make things better.