The 24-200 is very dependent like a lot of modern lenses on software. The results were horrible in DXO, I could not get capture NX to work for me, but I get nice results in Capture 1. I think much of your disappointment might be a question of lens profiles, especially concerning CA problems. Agreed CA's are the weak point of this lens.I have a dog in this race since I swapped from an EM1.2 to a Z7 this summer but subsequently decided to swap back! My primary use is landscape. I used the 12-100 extensively with the EM1.2 and bought the 24-200 on the Z7 to give me much the same capability. The lenses are about the same size and weight. I also had the 14-30 and the 24-70 f4 lenses for the Nikon. The 14-30 and 24-70 I found to be absolutely superb. Very sharp over very nearly all the frame, even wide open. The 14-30 did suffer from some loss into the corners, but it was not a deal-breaker.
However, I was a bit disappointed in the 24-200. It's by no means a bad lens, but it's not as good as the other two, esp near the long end, and it feels like a cheap lens in comparison. In fact, compared to the Oly Pro lenses, none of the Z lenses felt as good (but of course this is just subjective and counts for nothing in the final result). There is also a lot of purple fringing on the 24-200. On top of all that, the Sync IS on the Nikon is a long way behind that on the EM1.2 + 12-100. Looking at other alternatives at 200mm with the Nikon, there was only the 70-200 f2.8, but that's just huge (and expensive)!
On top of all that, I missed the Oly camera's features, speed, and ergonomics. And although the NIkon files are certainly better, I didn't find it was making that much practical difference to the output I was producing (mostly on-line with some A2-sized prints).
So, whilst I thought the Nikon was a very nice camera, it wasn't the silver bullet I thought it might be and that actually I just preferred shooting with the EM1.2.
Frankly, the lightweight build does not seem cheep in my opinion, sure it is not comparable to my old Nikkor 180 2.8 for build quality, maybe it is the use of lightweight modern plastics that give an impression of "cheapness". The 24-200 lens is my go to lens for hiking and travel. Any optical defects are made up for by the practicality of this lens.
It reminds me of the problems I had matching the Panasonic 12-35 to the EM5. Only DXO seemed to be able to cure the green blue fringing. Once the camera lens and software triangle was perfected, it was a brilliant combination. But the out of camera JPEGs were horrible.
For me, getting past lens sharpness measurements, I have far more post processing control over the Z7 files. I think the quality and malleability of the large Z7 files are the main reason for going Nikon Z. I also am able to use my old Nikon Ai glass on the format it was designed for.