Although the A6400 will not "officially" have animal Eye-AF until the new firmware is released at mid-year, my A6400 seems to recognize Lynn's face as a "face" and hones in with Eye-AF. BTW: the new firmware release for the A9, A7iii and A7Riii has Animal Eye-AF included along with a general upgrade of auto focus capabilities... I encourage anyone who owns one of these cameras to upgrade the firmware and take advantage of the improved focusing system...
Animal Eye-AF is a ball with which to shoot just as human Eye-AF is great fun to use. I shot these with my A6400 and the Sony 70-200mm f/4 G OSS lens which is a wonderful combination... Although I normally shoot my Canon 70-200mm f/4L IS lens with the tripod ring attached, I remove the tripod ring from the Sony lens because it seems to balance a bit better that way on my tiny A6400.
Do I absolutely need animal Eye-AF? Heck no! However I don't "absolutely need" internal metering, interchangeable lenses, or a focusing coupled to the camera... My first cameras dis not have those niceties... But, would I buy and use a camera in the 21st Century that doesn't have internal metering or focusing and did not have the capability to change lenses - not only no but, HECK NO!