I have a Z5 with a nearly identical sensor. OK, it doesn't have the backlit feature, but that only makes a difference in low light conditions.
Anyway, I have tried mine in DX mode. The only reasons I could see for using it is, number one, to use a DX lens. Actually, you don't have a choice here, I believe it automatically switches to DX mode with a DX lens installed, and won't let you choose. The number two reason would be to take advantage of the 1.5 crop factor. What I ended up discovering was that there was no real difference in quality between using the DX mode and cropping the FX image in post processing to match magnification. I did find the DX mode images had more detail than I expected.
There did seem to be an increase in using the same FX lens on a crop frame camera of the same MP rating.
I compared some 500mm images using my 200-500mm F mount lens on the Z5 with FTZ adapter and cropping them to match an effective 750mm image. I then took pictures of the same subject using the same lens on my D3400 (24 MP crop sensor). Comparing the two, the D3400 seemed to have a slight edge in resolution.
Bottom line, I don't see any need for me to use DX mode. I am open to differing opinions.