No, it's not true all around the US. There are plenty of places where if somebody buys a property, it's theirs to do what they want within with rules set by the government. There are places in Texas, for example, that don't even have zoning laws. The interference by local communities is not a universal thing.
Texas still has deed restrictions that prevent corner stores in residential neighborhoods, density restrictions, buffering ordinances, historic preservation sites, lot size restrictions, and other things like work similar to zoning laws.
