You're saying that the role of government is to intrude into the interrelationships of the individuals who are citizens to protect the "common people" from the "wealthy and powerful".
You're putting words in my mouth again. Whether the government needs to "intrude into the interrelationships of individuals" depends very much on the material circumstances and the complexity of society.
There are certain things that a government MUST do in a complex, industrial economy, that it does NOT have to do in a simpler agrarian economy. In the simpler arrangement, government intrusion is, more often than not, on behalf of the wealthy and powerful, to uphold the privileges of the landed elite, to enforce laws that provide forced labor of one kind or another, to exclude ordinary people from land ownership or from entry into business. For the most part, in a situation like that, liberalism calls for the government simply to refrain from doing these things. That's an oversimplification, but it's largely true.
In a complex, industrial society, the government MUST set trade policy, labor policy, industrial regulations; taxes are higher because there is more wealth and greater demand for public services, so tax policy is more important in its effect on people's lives; most people make a living working in a paid job rather than owning their own farms or small craft businesses, so regulations affecting labor rights and obligations are more important, too.
These are not areas where the government has any option of simply not "intruding." It MUST set trade policy, labor policy, tax policy; it must build infrastructure, fund education, manage health care; there are a great many things that the state must do in an advanced, modern economy that it does not need to do (and often couldn't do even if it wanted to) in a poorer, simpler, more decentralized, agrarian economy.
What matters to a liberal in a situation like that is
on whose behalf the government does these things that it MUST AND WILL do, one way or another, regardless.
A liberal wants the government to set all these policies with a view to protecting ordinary people from the rapacity of the rich and powerful. A conservative wants it to set all these policies to benefit the privileged.