The
Laffer Curve is a simple way of pointing out a basic reality. If you have a 0% tax rate or a 100% tax rate, you will get the same amount of revenue...none. Somewhere between those two poles is the ideal rate of taxation for maximizing revenue. What it illustrates is that the higher you raise taxes, the more you discourage productive economic activity. Income taxes are a tax on work. If you raise them high enough, people will not do work beyond the point at which they gain no benefit from it. That slows down the economy, which in turn results in less revenue.
So cutting taxes increases revenue to the degree that it spurs economic growth...which it
always does. The debatable question is
how much revenue is gained or lost in either direction, and therefore what the ideal rate is...and that is a very difficult thing to pinpoint.
Tax policy is not by any means the sole determiner of economic growth, but it is, without a doubt, a significant component. Your statement that "Economic growth happens totally independently of government policy" is extremely inaccurate, if taken at face value. When you consider all of the ways the government interferes with the economy, and in particular when you examine how various policies play out in different countries, it is undeniable that government action can have negative effects on economic growth. If what you mean is that government cannot create economic growth, you're correct. But it can definitely destroy it. And so, policies that remove the government boot from the economy's throat can be said to spur economic growth, even though they are merely removing impediments.