So, theoretically, if Nikon wasn't nice enough to reduce the sensor
size, when putting a DX lens on an FX camera the reverse would be
true the 18-200 would really be a 12-133.
No, the 18-200 would still be a true 18-200. I think you need to start forgetting about crop factor for a minute. An 18 mm lens produces exactly the same image on a DX sensor as it does on an FX sensor. If you think of the DX sensor as a masked-off FX sensor, then you see that the lens projects the same size image no matter what sensor the light eventually hits.
Try to think of your lens as a projector, and the sensor as your screen. Imagine your screen measured 36 feet wide by 24 feet high. That's a full frame screen(sensor). Imagine now that you have a projector, which is able to throw a beam of light wide enough to cover the whole screen with an image. That would then be a "full frame" projector(lens). Say you needed a "50mm" projector to make the beam of light shine on the entire screen. There's your favourite scene of a movie, where Clint Eastwood's head fills the screen from top to bottom, with his chin just above the bottom of the screen, and the top of his head just below the top of your screen.
Now imagine that during the night, some vandals broke into your cinema, and cut away the outer edges of your screen(sensor), leaving you with only the central area measuring 24x15 feet? Using the same projector, the image on the screen is exactly the same size. However, now that the screen is smaller, the central portion of the image now fills your available screen area. On the screen you have left, Clint's eyebrows are now at the top of the screen area you have, and his upper lip is now the lowest part of his face you can still see. Because the screen is so much smaller now, it SEEMS as if the director had zoomed in. But he hasn't - it's just that the cropped format of your vandalised screen (sensor) gives a zoom effect. That's why a DX sensor gives a zoom effect compared with an FX sensor. It happens even with the same lens, which in our analogy is the projector.
Now imagine that you are bored one day, and decide to cut a hole in a piece of cardboard you took from a cornflakes packet. You now hold that up in front of the projector in your cinema. It just so happens, that you've cut the hole just the right size, and you're holding it at just the right distance from the projector that you block off ALL the light that would have fallen on the missing parts of your vandalised screen. The projector now can only throw light onto the 24x15 foot area where the remainder of your screen is. You've restricted the image circle of your projector. Not that it's still the same projector, and you haven't changed it's focal length at all. You've narrowed the angle through which it can project light. That's ALL a DX lens is. A lens where the angle of view is restricted, so that light doesn't fall outside the area of your small DX sensor.
Now imagine that you've mounted that piece of cardboard with the hole in it in front of your lens permanently, because it reduces the amount of stray light landing outside your screen area. One day, the vandals see the error of their ways, and they decide to buy you a new screen that is the same size as it was originally - that is, 36x24 feet. They break in again one night, and mount the new screen perfectly.
The next day, you go into your cinema and watch a movie. Then you realise that your screen is back to it's former glory. But hang on - the outer areas of the screen are dark! That's because you've blocked off the light that would have hit those parts of the screen with your cardboard mask that reduces the image circle. That's what happens when you mount a DX lens on a full frame FX sensor. In order to get the full picture, you need a full frame lens. In our analogy, you could just tear down your piece of cardboard with the hole in it. In the real world, you need to swap your DX lens for a full frame FX lens.
Do you see that no matter whether you mount a DX of FX lens, and no matter whether you have a DX of FX sensor, an 18mm lens will always throw the same size image onto the sensor of a subject a fixed distance away. The same for a 50mm lens, and also the same for a 500mm lens. It's just that when you use a DX sensor, irrespective of whether you're using a DX or FX lens, your image appears to be magnified because the sensor is smaller.
I hope that helps you, because when I was first thinking about the relationship between DX and FX lenses and sensors, that's the analogy that made it crystal clear in my head.
But using a non-DX lens on a DX camera gives you the added bonus of
the 1.5 crop factor. Becaus they have been built with a larger sensor
in mind.
Nope - and if you understood what I've written above, you'll now understand why.
Amy