What many people don't seem to understand is the tradeoff between DOF and light-gathering ability. You sacrifice DOF to get the extra stop of light. If you need that DOF back, then you need to stop down on FE and lose that stop.
There's no such a thing as 'sacrificing DoF' in a general sense. You can change distance, max aperture or FL to get the DoF you need, you don't have to adhere to the artificial construct of using the same lens with the same distance, FL or FoV.
There is no 'correct' or 'most desirable' DoF. It's as relative as your composition. The same way that there's no one correct FL.
There's also no 'FE'. That's just what Sony terms its lenses that are FF compatible. It's not a mount and it's not a sensor format reference like 'FX and DX'.
You can lose focal range if you go with an 18-55 compared to a 16-70, and there you actually do have a 'loss' of a tangible nature. Similarly, you can have a lens with smaller maximum aperture, like F4 vs. F2.8. Optical performance equal there, you're losing flexibility. But a FF body itself has a greater range for control over DoF, not less.
I agree that a lot of people don't consider this ... but it's also not always a consideration. A lot of photography is done at base ISO, whether from a tripod, using IS, or simply in good enough light to use fast shutter speeds, and you can stop down to your heart's content without having to raise ISO. Look at how much photography was done over the years preceding digital with Kodakchrome or Velvia.
I'm not saying that high ISO isn't a great thing - I shoot about 40% of my photos at or above ISO 1600. But depending on what you're shooting, you can exploit larger sensors and still have all the DOF you need.
I'm not sure I follow your point unless you are arguing that full frame at ISO 100 is better tan APS-C at ISO 100, which is only barely true. Look at Samsung's or Nikon's most recent APS-C cameras' dynamic range for instance. Even the a6000's ISO 100 DR is very close to the a7 series.
It's close relative to prior generations of APS-C cameras and the gap is indeed narrowing, but it's still a detectable difference. The A7 series produces superior tonal, dynamic range and SnR across the ISO spectrum.
You can't change the physics of the larger capacity light wells.
There are certainly real reasons to go with smaller sensor cameras, but that's predominantly relating to size, weight and price. In the case of the A6000 vs A7 series, AF performance is better as well.
