I don't think so.
Mirrorless is just starting, the amount of a7x vs the amount of full frame DSLRs outthere is just very tiny, probably no more than 2-3% at most.
The DSLR replacement market is there to be taken and the best solution is going to win.
Probably more like 10% if you're talking about full-frame only.
Thing is, Sony owns 100% of that 10%. And, more significantly, the percentage of
new sales is far more than 10% - at the moment, they are not selling 9 full-frame SLRs for every one full-frame mirrorless body. Most of that 90% is made up of pre-existing/legacy bodies.
The early start Sony took is good, but I believe it has also helped Nikon and Canon understand what they could do better. The a7x for sure have some loving customers, but they have also many users unhappy about the experience. They are far from perfect cameras and the system as a whole is even less perfect.
Sony's experience may help Canon and Nikon get started more quickly, but it has helped Sony even more. It's not like Sony doesn't also know what else could be improved. And, from their own experience, they would also know how to do it.
Expect future Sony bodies to be more A9-like and less A7-like, with improved weather sealing and connectivity. Looking at the trend since the launch of the initial A7, you can expect them to increase in width and height to something similar to an SLR (probably D7500 dimensions rather than D850 dimensions), but retaining a saving in depth, since there is no need for a mirror box. Expect the weight to be more like 700-800g, instead of the A7r3/A9's 600-700g or the D850's >1kg. But expect them to use the increase volume and weight to deliver performance, not just empty weight or bigger batteries.
And that's just the camera bodies. The lens incumbency is probably even more important, since lenses tend to stay around for several cycles of bodies. Sony has all the major bases covered (superteles, tilt-shifts and fast medium-teles (e.g. 200mm f/2) are still to come, but they represent a very small proportion of the overall market). Unless the Canon and Nikon bodies launch with a new 24-70 f/2.8, 70-200 f/2.8, some sort of fast UWA zoom and an 85 f/1.4 (or similar), they will find it difficult to make significant headway until those bases are covered, regardless of what the bodies are like.
There is clearly room for improvement and both Canon and Nikon have a very large base of users who would rather stay in the family because it is likely to be cheaper.
Sony also knows how to price-match. They can ask what they do now because there is no competitor. When there is one, they will reduce their prices, like everyone else. Remember the prices of the early Canon full-frame SLRs, before Nikon started making them?
Both companies do also IMHO have superior lens technology, better tracking AF algorithms, a better understanding of ergonomics, better weather sealing, better ruggedness,...
Lens technology is arguable. Sony certainly knows how to design them well - on paper, they are as good or better than the others. Their manufacturing tolerances, though, probably leave something to be desired (which is probably what leads to such things as the 70-200 f/2.8 underperformance, and the 16-35 f/2.8's sample variation).
But the 12-24 f/4 is the equal of the Canon 11-24 (if not slightly better) and soundly beats the Nikon 14-24. The 24-70 GM is as good as any other 24-70 out there. The 100-400 GM is sharper than the Canon 100-400, and much sharper than the Nikon 80-400 - indeed, sharper at the same aperture than the Canon 200-400 f/4.
Better AF tracking? Certainly not in the case of the 1Dx2 - the A9 is right up there. Even compared to the D5, the A9 is not as
fast, but probably even more
accurate. As in, when tracking a fast-moving object, it will have more frames out-of-focus than the Nikon (usually lagging behind the subject's movement), but, when tracking a slow-moving object, it is more likely to remain focused directly on the targeted part of the subject rather than being slightly front- or back-focused (e.g. focused on the subject's ear, nose or eyelashes, rather than the eye).
And that is just 'dumb' AF - tracking a moving point in space, without any system knowledge of what it's actually tracking. Sony is well ahead in 'smart' AI - things like eye focus - which are only going to become more and more prominent in the future.
I'd say Sony understands plenty about ergonomics and ruggedness. Look at their video cameras. Just that the A7 series was designed - initially, at least - with small size in mind. But they are becoming bigger, heavier and more rugged, as they trade small size for increased usability. The A7r was 465g. The A7r3 is 657g. The trend will probably continue, up to around D7500-size. They wouldn't want to go too big, either. I'd much rather shoot an A7r3 or A9 than a D850 or D5 - the grip on those cameras is far too large, leading to a precarious grip. Many others are in the same situation. Not everyone has huge hands and difficulty manipulating small objects.
Yes, adpated lenses AF performance may not be good for all lenses, but then again few people need great AF performance on all their lenses. AF performance is basically irrelevant for anything wider than 50mm for example. So a majority of users would be fine with buying 2-3 mirrorless lenses and adapting their existing ones.
Think also that Nikon users would finally be able to mount some fine Canon glass without having to spend too much also. The major migration on-going from Canon to Sony would also be greatly slowed down and the need for Canon users to access good sensors has clearly helped Sony a lot move in faster.
Yes, Canon's sensor weakness was Sony's strength. If Canon's sensors had been up to scratch, I doubt the A7 series would have been anywhere near as successful as it has been.
But that won't be repeated. Sony's system doesn't have a fundamental weakness that they refuse to correct which can be similarly exploited by Canon and Nikon as they launch their mirrorless systems. The 'leakage' to Sony may slow, but won't stop until Canon and Nikon both manage to match Sony in mirrorless body capability and lens offerings. Unless they make a major effort and launch 6 high-end lenses at the same time, this is unlikely to happen for a few years.