Most of those cheaper machines ship from china, and shipping (and tariffs) is not included in those prices. Shipping can be a significant additional cost (there is usually no shipping included on any of the machines prices). They will also come with little to no documentation, training or support. Depending on your experience and knowledge, these can be very important. Those with "free" shipping is usually only to the nearest ocean port - you will be responsible for picking up from port (and paying any tariffs due) and shipment to your location. Not too bad if you live in Long Beach, more of an issue if you live in Denver.
The automation technologies machine is one of the Chinese machines, but imported by a US company that will provide documentation and support.
CAMaster is US built, well documented and well supported, with factory training available, which is why it has been recommended.
There are other options in the price range, including shopsabre or shopbot. One option you may wish to consider is a kit machine from CNC Router Parts or Fineline Automation. You would need to assemble yourself, but they are good machines at a lower price.
Note that 3D carvings are very time consuming, especially one anywhere near the 4 x 4 size. They can easily take 20 hours or more. The more detail you want (and the smaller bit used to cut it) the longer it takes. Here the speed of the machine can play a big role, a machine that can 3d carve at 400ipm will take much less time than one that can only do it at 100ipm. Do not be mislead by the quoted "rapid" speeds, try to find cutting speeds.
When David asked about the rest of the shop, it was referring to tools to prepare large glue ups (need to be able to joint and plane and cut boards to size before glue ups, or before putting onto CNC. You will also need dust collection (a vacuum won't be enough). Also most of those machines require 220V power. Most people would not want them in the house (probably can't fit through anything smaller than a garage door anyway). Off the machine, you will need to sand and apply a finish to create a finished carving.
How are you intending to create the artwork (designs) to cut? Some of the software to create 3d models runs $1600 and up, and there is a signifiant learning curve. Between the time it takes to create the files, and the time it takes to run them, such carvings must often sell for a considerable cost to represent a reasonable return.
My DIY machine has a cutting area of 49" x 60" and cost me $2800. You will not get anywhere near that price buying commercially.
Tubular latex pressure vessel configuration engineer