Sony already have stills cameras and pro video cameras for their E mount. I judge Sony's current engagement in their DSLR A mount to be a service to existing A mount users, rather than a strategy for the future.
Sony has begun reworking the UI, with a new menu system in the A6500 camera. A touch interface has started evolving as well.
Nikon service and support in Norway has been staffed down from 13 to 3 persons in Norway, according to Frank's link. Where is this excellent service and support organization that Sony would get by buying Nikon?
Nikon is weak on video, no really good video AF (no LV PDAF nor dual pixel like Canon), no EVF option, no focus peaking. Nothing for Sony in the video department
Nikon has fast AF for sports and action with long lenses with the D5 and D500, particularly tracking is excellent. This is the only thing where Sony is behind with the E mount. The A mount A99 mkII is much closer to Nikon in performance here, but there is a much smaller selection of long lenses than for Nikon.
Lens design, Nikon, Sony and Zeiss are all capable of making great lenses and they do so. Canon, Leica, Fujifilm, Olympus, Cosina (Voigtländer), Panasonic can all be added to that list. So no gain is to be had here by a merger of Sony and Nikon. Sony is already outputting as many or more new lens models per year for the E mount than Nikon does for the F mount.
Lastly, Nikon management appear to me to be bad, and I wouldn't want any Nikon management people to work with the Sony E mount system. Period. Just see how they have botched the Nikon 1 system, the DL launch, Snapbridge, Keymisdion. This is to be blamed on management rather than the engineers. Nikon engineers just made the 105/1.4 and the 19/4 PC-E.
The parts of Nikon worth having for Sony is the Nikon lens designers and the Precision equipment division. The rest not, I think. Sony does lens design well and Zeiss is on board, so that leaves Precision Equipment.
I don't think Sony should buy Nikon. Rather I hope that Nikon will find a partner that is strong on video, but currently isn't strong on stills cameras or lens development. Preferrably the Precision equipment division of Nikon should fit into such a partnership as well. Someone should evaluate Nikon management and take action on their findings.
Edit: Typos