I think you are thinking of an unlocked bootloader. Unlocked is whether the device is tied to a particular service provider like sprint or Verizon or cricket or any other. Those you can buy unlocked. Rooted is very different. Many service providers, especially Verizon and the phones provided with Amazon stuff built in have the bootloadera locked. Some can be unlocked by simple code requested after the phone is paid off, others won't unlock them and you need to hope a way is found. XDA folks have ways to unlock the bootloader for many devices that the manufacturer doesn't want unlocked.

To root your phone you must have the bootloader unlocked, so buying an unlocked one saves that step, but you must still root the device to access those benefits.

Rooting your phone is basically like using a windows PC on an administrator account versus a severely limited user account. It vastly increases what you can do with the device, not just who you can choose as your service provider. While a factory won't sell a rooted phone directly that I can think of, there are sellers on eBay that sell rooted devices.