What do you think would be the difference between shooting a 20mp DX camera with a lens, then putting that lens on a different camera with enough pixels that the DX crop from it is also 20mp?
Perhaps you could be more specific with the detail of your question.
OK, what is the difference shooting a lens, let's say a 300f4, on a D500, then putting that lens on a D850 - at the same subject distance, just swap cameras under the lens, then crop that shot to DX. You get a 20mp D500 image and a 19mp D850 image. And dof should be exactly the same, since shot from the same distance.
If you switch from FX to DX with the same lens the angle of views changes - and you do not get the same image :-D
If I shoot two different lenses from the same spot, the images are different. So what's the point? Anything optically I can do with a 300F4 on a D500, I can do with a 300F4 on a D850 in DX mode.
I'd link to a webpage of mine where I shot the same lens on CX, DX and FX cameras and compared the results, before and after cropping. But right now I'm fighting some equipment issues in my network and my web server is down.
If you use a wider angle lens on DX to get the same angle of view as an FX then the DX image has about one step more depth of field than the FX image.
Yes, but then I'm not shooting from the same distance.
I do use this 'trick' a bit, by the way, with my underwater macro shooting. Basically I shoot at F16 from a distance, then crop. That way I have less pixels on subject than if I'd gone in closer, but I have more DOF, and less diffraction from stopping down to, say F29.
If you use the same lens on both format bodies and crop the FX image to DX proportions you'll near enough the same depth of field.
Yep.
For a more exact depth of field change the DX crop would need to be 1.42 rather than 1.5. The difference I consider minor.
I used to shoot film (from about 1960 to 1992), then DX until 2007 or so when I got a D700. At that point I had to take my old lenses out and relearn how they behaved on FX, mainly for depth of field. I quickly came to the viewpoint that for the DOF to look 'the same' on both bodies, with the same lens, I had to stop down another 1.5 stops on the FX side. (Or move and crop...)
What REALLY caused me concern was what it looked like when you pixel-peeped the corners. By the time I got a D800e a few years later, I resolved to also upgrade my old AF/AF-D lenses to the newest standards. Much improved results, both wide open and in the corners.
If you use the same focal length lens on both bodies with no FX body cropping then the narrower angle of view on FX loses you two stops depth of field compared to the one stop dof gain with the DX body.
One could also say 'gains a couple of stops of subject isolation'.
Shooting this way overall you lose one stop dof on DX, offset by greater subject magnification.
Nowadays I shoot a Z9, and before that a D850, for the same basic reason. These cameras may not be the best at a particular thing, but they'll shoot almost anything. Jacks of all trades, and quite good at almost all of them. I can (with the Z9) shoot faster than a D500. I can set the Z9 to DX mode, and even the viewfinder will then 'DXify itself'. Pretty much same resolution.
I do crop a lot, but almost always in post. Because I crop so often, I no longer really think of formats. I just frame as close as I can (very often cannot approach underwater subjects for macro to fill the frame), and then crop where I need to to get the composition I had in mind. Or another composition that seems better in post. I don't think in terms of 'on a DX camera this 300f4 becomes a 450F4'. I just look at the end results after I've cropped and decide if I need to change lenses. However, underwater I have unique challenges in that very few lenses are supported. I know that I normally shoot at what would be close to full-frame with a 150mm macro - but I can only have a 105mm, so I end up cropping a lot.
Getting back to the question in the title = do I have a reason to do DX? Basically only for cost. I can do what a DX camera can do with the D850 or Z9, simply by 'post-cropping' instead of 'pre-cropping'. But I can't do with a DX camera what I can do with FX, though I can do a lot of the same things with a smaller camera.
There is another reason, among so many, that I often need to crop. Recently I bought a strobe with a snoot, and it is so difficult to line up on a subject that it is quite routine to shoot a portrait-mode subject in landscape and then crop to portrait in post. It's just too difficult to reorient things from landscape to portrait. (It can take several minutes to line things up for an orientation, and even then you have to precisely position that flash for the small circle of light to hit the subject. Anyway, here's a shot I simply could not get without cropping once I'd set up for landscape.

Snooted strobe image of a Christmas Tree Worm shot in landscape and cropped to portrait orientation
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Phoenix Arizona Craig
www.cjcphoto.net
"I miss the days when I was nostalgic."