So even if you had your unregulated capitalism full of shacks and slums, it wouldn't take many centuries before rich crawl into government power to "fix it".
This is exactly why your government has a constitution. Sadly, your founding fathers fell far short by not adding strong property rights into your bill of basic human rights.
Imagine if your 5th amendment read like this:
No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces, or in the Militia, when in actual service in time of War or public danger; nor shall any person be subject for the same offence to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation.
The right of every person to acquire, possess, peacefully use, improve, rent, and voluntarily convey property shall not be infringed, except by restrictions necessary to prevent demonstrable injury to the equal rights of others.
Private property shall not be taken, nor its sale compelled, for transfer to or use by another private person or corporation. Increased tax revenue, economic development, or the preservation of another’s property value shall not alone constitute public use or justify restrictions upon these rights. The peaceful production and consumption of goods upon one’s own property for personal or household use shall not be prohibited or penalized merely because such conduct, individually or in the aggregate, affects commerce, prices, or demand. Nothing herein shall prevent restrictions necessary to protect others from demonstrable risks of poisoning, fire, explosion, pollution, or other physical injury. Effects upon prices, competition, supply or demand shall not alone constitute such injury.