From my point of view, 3d in Flash has never taken off completely, because of the decisions of Adobe and the industry's desire to turn towards html5.
At the beginning of 3d Flash, there was a boom, and many things were done in 3d. Among them several 3d engines + developments.
But there were several decisions at specific points in time that undermined the immense potential it had to wipe out the entire industry:
2011 - Flash out of mobile browsers;
Another very important (I do not remember the moment, but maybe 2013), Adobe stops developing the next generation of Flash AVM. (This might indicate to some developers, that Flash had no future);
In 2014, Adobe reported that Flash Player was going to be abandoned from browsers in 2020.
At the same time, the entire industry (large corporations, "tech" journalists, blogs, street people ...) was against Flash, as it turned towards html5.
On the other hand, 3d is more "difficult" than 2d. More human resources and larger projects, usually.
All this added, is what caused many developers to abandon Flash, and therefore, is what caused the 3d in Flash to fail.
There is only a small part of truth in that it was more complicated to make the 3d work well in mobile. But this is much less than the other reasons. According to the device, there were decent developments (Unity also had its problems in slow devices). And there was the potential to improve the platform.
If 2d is still working in the Flash world, it is because it is easier to tackle and because of the inertia of the developments for so many years.
If Adobe had continued betting on Stage3D in all areas, without abandoning the technology, today 3D would be in the stellar state. And Unity would have only a small niche market. They started off with a lot of advantage when they released Stage3D (Flash was infinitely more extended than Unity).