The eternal IQ vs convenience trade-off! My latest random thought is to get the 24-200 to use until we see what the promised 24-105 behaves like. Given the performance of S line lenses so far I expect good things. The 24-200 could well be a keeper even then for times that call for a one lens solution.
As for the 70-x00 solution, I bought the 70-200 f/4 when I was shooting DX — a great lens. However I found it to have lots of overlap with the 24-120 and not enough telephoto reach on FX. I ultimately sold it and picked up the AF-P 70-300, which is a bit slower, very sharp, gives an additional 100mm of telephoto reach, and is both lighter and more compact than th 70-200 f/4. So far, no complaints...
As for the 70-x00 solution, I bought the 70-200 f/4 when I was shooting DX — a great lens. However I found it to have lots of overlap with the 24-120 and not enough telephoto reach on FX. I ultimately sold it and picked up the AF-P 70-300, which is a bit slower, very sharp, gives an additional 100mm of telephoto reach, and is both lighter and more compact than th 70-200 f/4. So far, no complaints...
Dave