Coase's argument was that "given 0 transaction costs," it doesn't matter who owns what property or right. The market will achieve efficient solutions as firms sell each other radio spectrum or whatnot. Policy should focus on minimizing transaction costs and let the market organize itself.
Circa 2005, I heard a podcast with 90-something Ronald Coase. He has pissed. Everyone had been teaching his theorem backwards for decades, backed with the "chalkboard economics" he despised.
What Coase actually meant is that (1) transaction costs tend to be high (2) this explains the clearly observable inefficiencies of such markets. Literally the opposite of what I was taught as "Coase Theorem."
He meant that because market are imperfect, it really matters what the starting position is. Trickle down economics is the same kind of error. If we are extremely confident that markets work the way efficiency-assuming models do... Trickle down makes sense. It doesn't really matter where the money starts, the market will deal with allocation efficiently. If not it does matter where the money starts.
In any case, the "wealth disparity" discussion is almost always badly anchored. The first thing to understand about wealth disparity is that it maps pretty much to wealth. More wealth, more wealth disparity... almost universally. Many or most people have no wealth, depending on your semantics of "wealth." Therefore, if the value/quantity of wealth rises, wealth disparity rises.
The actual equality dichotomy is ROIs vs labour/income.