The bottom line is, small and light can win the consumer/backpacker crowds, but you won't win over professionals until you can deliver the capability in the areas that matter to them. They've managed this with sensor performance (hence winning over lots of landscapers and non-action shooters), but, if they want to move beyond that, they will need to deliver performance beyond just the sensor. And that means fast AF, lag-free viewfinders and fast lenses, and likely a body size similar to the D810/5Ds.
If I was starting out competing with Canon/Nikon, I would think through "what is Canon/Nikons strengths and weaknesses, what is that people want and are willing to pay for. Is there an unexploited area that I can fill?".
Rather than go head-on in the fast-paced large-camera, tele-lens, sports area (where PDAF and the DSLR does quite well and Canon/Nikon have a large catalog of lenses), carving out a niche by being small while high sensor quality seems like an excellent strategy for competing on favorable terms.
It is not obvious that the number of "fast paced action shooters" in themselves are sufficient to generate a lot of profit for Sony. It may well be that Canon/Nikon have catered for this crowd because:
a) It was great for PR
b) It allowed them to try out new/expensive tech in smaller series/higher margin products first
c) Component re-use and market saturation made it wise to do so
However, a possible MILF-dominated market ruled by the likes of Sony, Panasonic and Samsung might be very different. They may have stronger ties to video, smartphones and social media. Shorter product life/less firmware updates. People running about with 800mm lenses on football matches may not sell as many Sony cameras as it used to sell Canon cameras.
The professionals are going to do what the professionals do. It seems that they are a quite varied group of camera users, prioritizing very different aspects. Arguing that "this camera is not professional" is (to me) sillyness. We all (most of us) have some profession, and I have to say that in mine I seldom treat my tools religiously. I'll use whatever is most convenient, costs less, gets the job done. If anything, I am more picky about the tools that I use for my hobbies.
It would be interesting to know how many consumers are willing to/have purchased a camera in the range of $2000-$3000 vs professionals. My guess is anywhere from 10:1 to 100:1. If I am right, then cameras like the A7 series does not _need_ to appeal to the "professionals" in order to be fantastically successful cameras.
-h