Equality of opportunity is a misleading term. 'Equality of process' I've found, is far better. I believe there is equality of process, but, there are immutable biological facts that result in the difference.
>In the case of a political election, the losing minority does not have their property instantly and compulsorily purchased at an arbitrary price set by the winner.
Perhaps not instantly, but it that's exactly what happens.
Government price controls do not fundamentally change the cost only the price.
If the government is so efficient and can, somehow, make housing cheaper than it would be in a free market why shouldn't they also take control of the food supply? Computers? Software? All industry?
If you're worried about the public good, there are nonviolent and consensual means of cooperation that I believe would make all of us far more prosperous than today.