After some research, the G7X appeared the 1" compact which was the best suited for my needs. But there is obviously a big sample variation so I ordered 2 of them (1 to be returned after a short trial).
Background
- I'm a M43 user and I never pixel peep except when buying a new camera or lens
- I never zoom 100% but I use an UHD monitor. When it looks good on my monitor, then it will be perfect for a A3 print (I never, never print larger, and don't plan to)
- So I evaluate everything on a 2160 basis (thus 8MP are always enough, actually)
- I shoot RAW and develop using Capture One Pro. Here, settings are defaults.
There are many things to evaluate in a camera. This review is very short and only focusses on the lens, because otherwise, the G7X is perfect !
Sample variation
I have two G7X II : one labeled as BLUE and the other one as PINK. I made several tests this afternoon. The shots are here :
When strong vignetting appears in an image of the gallery, it means that the lens correction is not applied, and that all the information on the sensor is displayed (wider, sharper). Otherwise, manufacturer corrections are applied. The G7X lens is more distorted than soft. Borders become softer when streched if distortion is corrected. But sharpness is much better without corrections. And in situations such as nature landcape, it perfectly makes sens not to apply corrections so as to a) keep a natural aspect b) keep shap borders. See https://www.dpreview.com/forums/post/59350760
The sample variation is obvious to me (without pixel peeping at all) : the PINK sample is the winner, hands down. It is particulary obvious when looking at the wide angle shots, with softer left sides of the BLUE sample.
Comparison with M43
I don't expect a compact camera beeing better than a M43 ILC camera, but it's only to state a reference point. I didn't put an ultrasharp PanaLeica prime on my GX80, but only a 14-140 superzoom (28-240 FF eq).
I only compare with the PINK sample (the best G7X II sample I own) :

The M43 is vastly superior to the G7X despite the lower M43 resolution of 16MP. Things are absolutely obvious even without zooming in. At least on an UHD monitor (don't know for a FullHD one).
Conclusion
Can a G7X replace an ILC, IQ wise ? No, not at all.
Is the G7X lens a bad lens ? I dont think so :
- it is longer and much faster than a RX100 or LX10 lens, so there is a tradeoff
- it is only very soft on the wide angle side ; results are OK IMO on the middle and tele side
but : the soft corners are not only soft @24mm. They remain so until 35mm, which is a lot. Sharpness will be decent for prints of a reasonable size, but it is not "4K ready".
Will I keep the PINK G7X ? Not sure about that. I'm still thinking because I like the G7X otherwise. I'm currently leaning toward sending back BLUE and PINK, and buy a Panasonic LX10 instead. I will miss the fast and long lens, but I'll get a much more capable AF and more sharpness.