The Sony A7 is able to adapt almost any type of auto-focus lens (Canon/Nikon/etc) and use autofocusing, but the auto-focusing is much slower than the same focal lengths native for the A7.
Why would a normally very fast focusing lens be so much slower, even when the Sony A7 has over 100 phase detect pixels?
With phase detect autofocus, it is possible for the camera to know more about how far out of focus an image is, so it can make a better guess of how far it has to move. If it knows how to get all the lens details, then it can quickly give instructions to move close to the target point. If it doesn't, then it has to more iteratively move the focus in to position until the proper spot is reached.
Additionally, PDAF sensors built in to normal imaging sensors tend to be a little bit slower and less precise than dedicated PDAF sensors due to their smaller size and more design compromises.
Both of these factors combine to make third party lenses much slower on a mirrorless body than on a first party DSLR with dedicated PDAF sensor.
When adapting non-Sony lenses to an A7, the electronic protocol for body/lens communication has to be translated as well. Between Sony and Canon/Nikon/etc. the commands to focus the lens are very likely to be incompatible, or are so radically different in how they're represented that the adapter has an issue translating them between the camera body to the lens quickly enough for good AF performance. This is why most adapters don't even offer autofocus. Reverse engineering one protocol is hard enough. Reverse engineering two and then translating between them is even harder.
You'd only get e-mount AF performance if the signalling protocols were identical and the adapter just had to do straight pass through of the signals.
For CDAF, the computer absolutely needs to tentatively alter focus to even arrive at any decision on how to proceed in focusing it - especially to ascertain in which direction to focus. Only closed-loop operation (doing and testing) gets any results here. It's like an operator trying to focus on a ground glass screen alone.
a PDAF system is more like an electronic rangefinder that supplies the computer with an estimate about how out-of-focus the image is, and whether it is focused too close or too far, before needing to do anything mechanical. This way, the coarse focusing can be done open-loop and in one step, only requiring closed-loop action to refine. It's like an experienced operator using a split prism rangefinder.
These two methods pose very different requirements regarding responsiveness, precision, speed, speed penalty of changing direction, hysteresis when changing direction, settling times/dampening... to a focusing drive train.
