The only way you've addressed it is by repeatedly (and ignorantly) saying that they exist. Constantly repeating it doesn't make it so.
Target, Wal-Mart, Costco, etal do not maintain "public spaces". They maintain spaces which they make accessible to the public, but which are controlled, 100%, by the management. If management deems someone to be a detriment to business, they have not only the ability, but the responsibility to remove that person regardless of the fact that they make the space accessible to the public...