Those reprap 3D printers are okay, but having done a fair bit of research an enclosed machine is much better and much more accurate.
Having an enclosed machine makes little difference to print quality. What it does do is reduce noise, shelters the printer from any draughts, provides some safety if kids are around and makes it look pretty.
The accuracy lies in the mechanical components. I.e. the rigidity of the frame, the type of printer (e.g. Delta vs. 3 axis), the stepper motors, the stepper motor drivers, micro steppers, ball screws/toothed belts, anti backlash ball nuts, software, auto leveling, extruders, print heads, heat beds etc etc.
There is a fair bit to consider when looking to buy or build a 3d printer.
I think you will find that having an enclosed machine makes a big difference to the print quality. The issue with open machines is cooling... If the parts cool too quickly they do not form correctly and the layers do not bond as they should, What i have learned is that open machines are good for small parts where the next layer is put down before the previous has had a chance to cool. But on a large part, such as this, the next layer will end up being laid on fully cured plastic so it would not adhere properly and would create a potential failure point.
What you have stated about the mechanics of the machine is not incorrect, however enclosed machines have huge advantages when it comes to controlling the environment which is very important when you are working with molten materials. Not really any different from painting, the best results are always achieved in a properly controlled paint booth and not inside ones home garage, although great results can be achieved from both, one takes significantly less post process work, and poses far less chance of failure.
My reference to 'reprap' specifically was only due to not being aware of any enclosed raprap machine currently available, and that one should look to another manufacturer for an enclosed machine.
The advantage to a reprap though is that they are open source, meaning that you can do with them what you like, and upgrade them as and when you want and print new parts for it to replace bits that you feel are poorly designed or to hold better stepper motors etc. It all gets very very technical when you dig into it far enough and is an awful lot of work to understand exactly how it all works and how to program it.